Highly Composite Number Calculator

Welcome to use the Highly Composite Number Calculator, which can quickly help you check if a number is a highly composite number.

Eg, Is 360 a highly composite number? Enter 360 into the input box and click Calculate button.

What is a highly composite number?

A highly composite number is a positive integer in which any smaller natural number has fewer factors than this integer.

For example, Is 12 a highly composite number?

There are 6 factors of 12, they are 1, 2, 3, 4, 6, and 12.

The natural numbers less than 12 are 1 to 11. Suppose Fn is used to represent the number of factors, then the number of factors from 1 to 11 are

The factor of 1 is 1. Fn(1) = 1.

The factors of 2 are 1 and 2. Fn(2) = 2.

The factors of 3 are 1 and 3. Fn(3) = 2.

The factors of 4 are 1, 2 and 4. Fn(4) = 3.

The factors of 5 are 1 and 5. Fn(5) = 2.

The factors of 6 are 1, 2, 3 and 6. Fn(6) = 4.

The factors of 7 are 1 and 7. Fn(7) = 2.

The factors of 8 are 1, 2, 4 and 8. Fn(8) = 4.

The factors of 9 are 1, 3 and 9. Fn(9) = 3.

The factors of 10 are 1, 2, 5 and 10. Fn(10) = 4.

The factors of 11 are 1 and 11. Fn(11) = 2.

It can be seen that the number of factors of natural numbers less than 12 is less than 6. So, 12 is a highly composite number.

The procedure to use the highly composite number calculator is as follows:

1Enter the positive number.
2Click Calculate button to verify whether the input number is a highly composite number.
3Click the Reset button to start a new verification.

Enter 144 into the input box and click Calculate button, as shown in the figure, 144 is not a highly composite number.

There are 16 factors of 120, they are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

There are 15 factors of 144, they are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.

120 is less than 144, but the number of factors of 120 is greater than the number of factors of 144. So, 144 is not a highly composite number.

Enter 360 into the input box and click Calculate button, as shown in the figure, 360 is a highly composite number.