How to Quickly and Easily Find All the Factors of a Number

Finding a number's components is a crucial math skill for basic arithmetic, algebra, and calculus. Those who divide a number perfectly include 1 as well as the number itself. To put it another way, every number is the sum of many factors.

Too Long; Didn't Read

The easiest technique to get a number's components is to divide it by the smallest prime number/integer (greater than 1) that goes into it evenly and leaves no residue. Repeat this method with each new number until you reach 1.

Numbers that are prime

Primitive numbers are defined as numbers that can only be divided by one. Prime numbers include 2, 3, 5, 7, 11, and 13. Because 1 is present in everything, it is not considered a prime number.

Rules of Divisibility

Some divisibility rules might assist you in determining the factors of a number. If a number is even, it is divisible by 2, which means that 2 is a factor. Numbers that add up to a number divided by 3 are divisible by 3 themselves, i.e. 3 is a factor in the number itself. If a number ends in a 0 or a 5, it is divisible by 5, implying that 5 is a factor.

If a number or integer is divided by 2, it is also divisible by 4, implying that 4 is a factor. If a number is divided by 2 and 3, it is also divisible by 6, indicating that 6 is a factor. If a number or decimal is divided twice by 3 (or if the total of the digits is divisible by 9), it is divisible by 9, i.e. 9 is a factor. Check Factors Checker Calculator to do this calculation easily.

Quickly Identifying Factors

Determine the number for which you wish to determine the components, such as 24. Find two more numbers that add up to 24. 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 24 in this example. This indicates that the 24 components are 1, 2, 3, 4, 6, 8, 12, and 24.

Negative numbers are factored in the same manner as positive numbers, but the components must multiply together to form a negative number. The components of -30, for example, are -1, 1, -2, 2, -3, 3, -5, 5, -6, 6, -10, 10, -15, and 15.

When you have a huge number, doing the mental arithmetic to identify its components becomes more challenging. Make a table with two columns and write the number above it to make it simpler. Using the number 3784 as an example, divide it by the lowest prime factor (greater than 1) that evenly divides it with no residual. 2 x 1892 = 3784 in this situation. Fill in the left column with the prime factor (2) and the right column with the other number (1892).

Continue in this manner, i.e. 2 x 946 = 1892, by adding both values to the table. When you get to an odd number (for example, 2 x 473 = 946), divide it by tiny prime numbers other than 2 until you discover one that divides evenly with no residue. 11 x 43 Equals 473 in this situation. Repeat the procedure until you reach 1.