Q:

What are the factors of 120?

A:

Quick Answer

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120. Using a simple set of tests allows the discovery of all of these factors in a relatively short amount of time, according to What Are the Factors.

Continue Reading

Full Answer

The first two numbers on any factor list should be the number itself and the number 1, which is a dividing factor for every number. Then, it helps to look at the last digit. If it is 2, 4, 6, 8 or 0, that number is divisible by 2. Dividing 120 by 2 yields 60, which becomes the fourth factor.

Testing a number's divisibility by three involves adding up the digits. In the case of 120, 1 + 2 + 0 = 3. If the sum is divisible by 3, so is the larger number. The number 120 passes this test, and so 3 is a factor. Dividing 120 by 3 yields the sixth factor, 40, according to Math Warehouse.

Testing divisibility by four requires running the test for two, dividing the number in half and running the test again with the product. If a number is divisible by 2 and then that number is divisible by 2 as well, the original number is divisible by 2², which is 4. Dividing 120 by 4 yields the eighth factor, which is 30.

Numbers that end in a 5 or 0 are divisible by 5, and so 120 passes that test as well. Running the division calculation yields 24, and so 5 and 24 are factors as well. Since 120 is divisible by both 2 and 3, it is also divisible by 6, and dividing 120 by 6 yields another factor, 20.

To test divisibility by 8, it is necessary to run the test for 2 three times. The number 120 eventually passes this test, and division results in another factor – 15. Finally, since 120 ends in 0, it is divisible by 10, yielding 12 and 10 as the final factors.

Learn more about Arithmetic

Related Questions

Explore