What are all the factors of 54? How to find the factors of number 54? Is 54 a prime or a composit number?
asked in Basic Math by expert

1 Answer

The number 54 has 8 factors.

The factors of 54 are: 54, 27, 18, 9, 6, 3, 2, 1

The square root of 54 rounded up to the nearest integer is 8. This is the limit to test our divisions because any number greater than 8 times 8 is greater than 54. So, we stop at 8.

Let's test the values 1 through 8 for division into 54.

  • 54÷1 = 54. Remainder = 0. So, 54 and 1 are factors.
  • 54÷2 = 27. Remainder = 0. So, 27 and 2 are factors.
  • 54÷3 = 18. Remainder = 0. So, 18 and 3 are factors.
  • 54÷4 = 13. Remainder = 2. So, 13 isn't a factor.
  • 54÷5 = 10. Remainder = 4. So, 10 isn't a factor.
  • 54÷6 = 9. Remainder = 0. So, 9 and 6 are factors.
  • 54÷7 = 7. Remainder = 5. So, 7 isn't a factor.
  • 54÷8 = 6. Remainder = 6. So, 6 isn't a factor.

Factors of a number n are numbers that can divide n without remainder, ie, remainder = 0. So, choosing only the numbers that meet this criteria from the list above, we find that the numbers which divide 54 (including 54) with no remainder are: 54, 27, 18, 9, 6, 3, 2, 1.

So, the factors of the number 54 are: 54, 27, 18, 9, 6, 3, 2, 1.

A composite number has more than two factors. A prime number has only two factors: 1 and itself. The number 1 is neither prime nor composite.

Because the number 54 has 8 factors, it is termed a composite number in mathematics.

As 54 is a composite number, we can factorize it, ie, express it in prime Factors as follows.

By factorizing 54 we get: 54 = 2 × 3 × 3 × 3.

Ie, 54 can be expressed as a product (factor string) of prime numbers (2 × 3 × 3 × 3).

answered by questiun