Mathematical Calculators

Factor Calculator

Find out the factors of any number with our factor calculator

Enter one or two numbers:

 ◦Divisibility rules for numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 ◦Divisibility rule of 7 ◦What is Prime factorization ◦List of factors by number
Factors are positive integers that divide into a given number exactly, with no remainder. In other words, if a number is a factor of another number, it can evenly divide into it. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because all of these numbers divide into 12 without leaving a remainder.
To find the factors of a number, you can use the divisibility rules, which are a set of shortcuts that allow you to quickly determine whether a number is divisible by another number. For example, if a number is divisible by 7, the last digit must be 7, 0, or a multiple of 7.
In addition to the divisibility rule for 7, there are also divisibility rules for other numbers such as 2, 3, 4, 5, 6, 8, 9, and 10. These rules can be helpful when trying to find the factors of a number, as they allow you to quickly eliminate numbers that are not factors.
Other areas of interest related to factors include prime numbers, which are numbers that have only two factors (1 and themselves), and composite numbers, which are numbers that have more than two factors.
To find the factors of a specific number, you can use an online factor calculator or perform the calculations manually. To use the calculator, simply enter the number you want to find the factors of and the calculator will provide a list of all the factors for that number.

Divisibility rules for numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10

1: A number is divisible by 1 if it is any integer.
2: Any even number is divisible by 2.
3: A number is divisible by 3 if the sum of its digits is divisible by 3.
4: A number is divisible by 4 if the last two digits form a number that is divisible by 4.
5: Any number ending in 0 or 5 is divisible by 5.
6: A number is divisible by 6 if it is divisible by both 2 and 3.
7: To determine if a number is divisible by 7, take the difference of twice the units digit from the number formed by the remaining digits. If the result is divisible by 7, so is the original number.
8: A number is divisible by 8 if the last three digits form a number that is divisible by 8.
9: A number is divisible by 9 if the sum of its digits is divisible by 9.
10: Any number ending in 0 is divisible by 10.

Divisibility rule of 7

The divisibility rule of 7 states that if a number is divisible by 7, the difference between twice the units digit and the tens digit must also be a multiple of 7.
For example, consider the number 76. To check if 76 is divisible by 7, we perform the following calculation: (7 - 6) = 1. Since 1 is not a multiple of 7, 76 is not divisible by 7.
On the other hand, consider the number 49. To check if 49 is divisible by 7, we perform the following calculation: (4 x 2) - 9 = -1. Since -1 is a multiple of 7, 49 is divisible by 7.
To use this rule, you can simply perform the calculation as described above. If the result is a multiple of 7, then the original number is also divisible by 7. If the result is not a multiple of 7, then the original number is not divisible by 7.
• How do I find the factors of a number?
• What are the divisibility rules?
• What are prime numbers and composite numbers?
• How do I use a factor calculator?
• What is Prime factorization

Prime factorization is the process of finding the prime factors of a number. Prime factors are the prime numbers that can be multiplied together to form the original number. For example, the prime factorization of 12 is 2 x 2 x 3, because these three prime numbers can be multiplied together to form 12. Prime factorization can be useful in finding the greatest common factor or the least common multiple of two or more numbers.
For example, consider the number 60. One way to find its prime factorization is to divide it by the smallest prime numbers (2, 3, 5, 7, etc.) until the result is a prime number. Doing this, we get:
60 / 2 = 30 30 / 2 = 15 15 / 3 = 5 5 / 5 = 1
So, the prime factorization of 60 is 2 x 2 x 3 x 5, or 2^2 x 3 x 5.

List of factors by number

You can use the factor calculator to obtain the list of factors below:
• Factors of 1: 1;
• Factors of 2: 1, 2;
• Factors of 3: 1, 3;
• Factors of 4: 1, 2, 4;
• Factors of 5: 1, 5;
• Factors of 6: 1, 2, 3, 6;
• Factors of 7: 1, 7;
• Factors of 8: 1, 2, 4, 8;
• Factors of 9: 1, 3, 9;
• Factors of 10: 1, 2, 5, 10;
• Factors of 11: 1, 11;
• Factors of 12: 1, 2, 3, 4, 6, 12;
• Factors of 13: 1, 13;
• Factors of 14: 1, 2, 7, 14;
• Factors of 15: 1, 3, 5, 15;
• Factors of 16: 1, 2, 4, 8, 16;
• Factors of 17: 1, 17;
• Factors of 18: 1, 2, 3, 6, 9, 18;
• Factors of 19: 1, 19;
• Factors of 20: 1, 2, 4, 5, 10, 20;
• Factors of 21: 1, 3, 7, 21;
• Factors of 22: 1, 2, 11, 22;
• Factors of 23: 1, 23;
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24;
• Factors of 25: 1, 5, 25;
• Factors of 26: 1, 2, 13, 26;
• Factors of 27: 1, 3, 9, 27;
• Factors of 28: 1, 2, 4, 7, 14, 28;
• Factors of 29: 1, 29;
• Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30;
• Factors of 31: 1, 31;
• Factors of 32: 1, 2, 4, 8, 16, 32;
• Factors of 33: 1, 3, 11, 33;
• Factors of 34: 1, 2, 17, 34;
• Factors of 35: 1, 5, 7, 35;
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36;
• Factors of 37: 1, 37;
• Factors of 38: 1, 2, 19, 38;
• Factors of 39: 1, 3, 13, 39;
• Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40;
• Factors of 41: 1, 41;
• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42;
• Factors of 43: 1, 43;
• Factors of 44: 1, 2, 4, 11, 22, 44;
• Factors of 45: 1, 3, 5, 9, 15, 45;
• Factors of 46: 1, 2, 23, 46;
• Factors of 47: 1, 47;
• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48;
• Factors of 49: 1, 7, 49;
• Factors of 50: 1, 2, 5, 10, 25, 50;
• Factors of 51: 1, 3, 17, 51;
• Factors of 52: 1, 2, 4, 13, 26, 52;
• Factors of 53: 1, 53;
• Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54;
• Factors of 55: 1, 5, 11, 55;
• Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56;
• Factors of 57: 1, 3, 19, 57;
• Factors of 58: 1, 2, 29, 58;
• Factors of 59: 1, 59;
• Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60;
• Factors of 61: 1, 61;
• Factors of 62: 1, 2, 31, 62;
• Factors of 63: 1, 3, 7, 9, 21, 63;
• Factors of 64: 1, 2, 4, 8, 16, 32, 64;
• Factors of 65: 1, 5, 13, 65;
• Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66;
• Factors of 67: 1, 67;
• Factors of 68: 1, 2, 4, 17, 34, 68;
• Factors of 69: 1, 3, 23, 69;
• Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70;
• Factors of 71: 1, 71;
• Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72;
• Factors of 73: 1, 73;
• Factors of 74: 1, 2, 37, 74;
• Factors of 75: 1, 3, 5, 15, 25, 75;
• Factors of 76: 1, 2, 4, 19, 38, 76;
• Factors of 77: 1, 7, 11, 77;
• Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78;
• Factors of 79: 1, 79;
• Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80;
• Factors of 81: 1, 3, 9, 27, 81;
• Factors of 82: 1, 2, 41, 82;
• Factors of 83: 1, 83;
• Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84;
• Factors of 85: 1, 5, 17, 85;
• Factors of 86: 1, 2, 43, 86;
• Factors of 87: 1, 3, 29, 87;
• Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88;
• Factors of 89: 1, 89;
• Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90;
• Factors of 91: 1, 7, 13, 91;
• Factors of 92: 1, 2, 4, 23, 46, 92;
• Factors of 93: 1, 3, 31, 93;
• Factors of 94: 1, 2, 47, 94;
• Factors of 95: 1, 5, 19, 95;
• Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96;
• Factors of 97: 1, 97;
• Factors of 98: 1, 2, 7, 14, 49, 98;
• Factors of 99: 1, 3, 9, 11, 33, 99;
• Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100;
• Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104;
• Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105;
• Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108;
• Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110;
• Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112;
• Factors of 117: 1, 3, 9, 13, 39, 117;
• Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120;
• Factors of 121: 1, 11, 121;
• Factors of 125: 1, 5, 25, 125;
• Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126;
• Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130;
• Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132;
• Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135;
• Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140;
• Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144;
• Factors of 147: 1, 3, 7, 21, 49, 147;
• Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150;
• Factors of 162: 1, 2, 3, 6, 9, 18, 27, 54, 81, 162;
• Factors of 169: 1, 13, 169;
• Factors of 175: 1, 5, 7, 25, 35, 175;
• Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180;
• Factors of 189: 1, 3, 7, 9, 21, 27, 63, 189;
• Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192;
• Factors of 196: 1, 2, 4, 7, 14, 28, 49, 98, 196;
• Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200;
• Factors of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210;
• Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216;
• Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225;
• Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240;
• Factors of 245: 1, 5, 7, 35, 49, 245;
• Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250;
• Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128, 256;
• Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270;
• Factors of 288: 1, *2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288;
• Factors of 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294;
• Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300;
• Factors of 343: 1, 7, 49, 343;
• Factors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360;
• Factors of 375: 1, 3, 5, 15, 25, 75, 125, 375;
• Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400;
• Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500; and
• Factors of 625: 1, 5, 25, 125, 625.
• How do I factor polynomials?

Factoring polynomials involves finding the factors of the polynomial that can be multiplied together to equal the original polynomial. There are several techniques that can be used to factor polynomials, including:
• Factoring out the greatest common factor: In this method, you look for the highest number that divides all the terms of the polynomial evenly. This number can then be factored out of each term, resulting in a simplified polynomial.
• Factoring by grouping: This method involves grouping together pairs of terms that have a common factor, and then factoring out that common factor.
• Factoring quadratics: Quadratics are polynomials that have a degree of 2, and can be factored using the quadratic formula or by completing the square.
• Factoring using the rational root theorem: If the polynomial has rational roots (roots that can be expressed as a ratio of two integers), then they can be found using the rational root theorem.
• What is prime factorization?

Prime factorization is the process of expressing a number as the product of its prime factors. A prime number is a positive integer that has no positive integer divisors other than 1 and itself. For example, the prime factorization of 12 is 2 x 2 x 3, because these are the prime factors that multiply together to equal 12.

What is a common factor?

A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because these are the numbers that divide evenly into both 12 and 18.

What are factor pairs?

Factor pairs are pairs of numbers that multiply together to equal a given number. For example, the factor pairs of 12 are (1,12), (2,6), and (3,4).
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.
Factor Calculator English
Published: Sat Feb 04 2023
In category Mathematical calculators

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