Easy Ways to Find the Factors of a Number

• Factors of a number are smaller numbers that can be multiplied to get the original number. For example, 2 and 3 are considered factors of 6 because you can multiply 2 and 3 together to equal 6. There are several easy ways to find some of the factors of a number.

One and Itself

• Although frequently overlooked, 1 is a factor because it can be multiplied by any number to get the same number. For example, 1 times 56 equals 56; therefore, 1 and 56 are factors of 56.

Two, Four, Eight

• Any even number, such as those ending in 0, 2, 4, 6 or 8, is evenly divisible by 2, which means 2 is a factor. Dividing 2 into the number also gives you another factor, the quotient, which is the result of the division. For example, 128 is divisible by 2, which means 2 and 64 are factors of 128.

  If the quotient is also divisible by 2, then you have two more factors: 4 and the quotient. For example, the other factors of 128 are 4 and 32. Four is a factor because you divided by 2 twice, and 2 times 2 equals 4.

  Likewise, if 2 goes into this second quotient, then you get two more factors: 8 and, in the example, 16. The 8 comes from dividing the original number by 2 three times, and 2 times 2 times 2 equals 8.

  This method can continue for bigger numbers to find the factors of 16, 32, 64, 128, and so on. Although the example is still divisible by 2, the result gives you factors that you have already determined: 16 and 8, so you wouldn't continue on.

Three and Nine

• If you add all the digits of a number and the sum is divisible by 3, then 3 is a factor. For example, if you add all the individual digits of 504, that is, 5 + 0 + 4, the result is 9. Nine is easily identifiable as having a factor of 3. Therefore, the original number (504, in this example) also has a factor of 3. You can also find the quotient for an additional factor, for example, 168.

  As was the case with 2s, if you add the quotient's digits together and the sum is divisible by 3, then you have two more factors: 9 and the second quotient, calculated by dividing the first quotient by 3. In the example, the digits of 168 add up to 15, which is divisible by 3. Therefore, we have two more factors: 9 (3 times 3 equals 9), and 56 (168 divided by 3 equals 56).

  The example stops there, because the sum of the digits of 56 are not divisible by 3. However, you could continue the methodology for larger numbers.