WorkedMathGlossary

Factors of 45

The factors of 45 are 1, 3, 5, 9, 15, 45. No, 45 is a composite number. Its prime factorization is 3^2 × 5.

Factors of 45
1, 3, 5, 9, 15, 45
6 factors
Prime or Composite
Composite
Perfect Square
No
Prime Factorization
3^2 × 5
Sum of Factors
78 (33 without 45 itself)

Factor pairs of 45

Every factor has a partner that multiplies with it to give 45. Listing pairs from the outside in is the fastest way to find all the factors: once the two numbers in a pair meet in the middle, you have them all.

PairCheck
1 and 451 × 45 = 45
3 and 153 × 15 = 45
5 and 95 × 9 = 45

Prime factorization of 45, step by step

Divide by the smallest prime that goes in evenly, then repeat on the result until you reach 1. The divisors you used are the prime factors.

StepDivideResult
145 ÷ 315
215 ÷ 35
35 ÷ 51

So 45 = 3 × 3 × 5, written compactly as 3^2 × 5.

Divisibility checks for 45

The quick rules a student uses before dividing, applied to 45:

Divisible byRuleFor 45Result
2last digit is evenlast digit 5no
3digit sum divisible by 3digits add to 9yes
4last two digits divisible by 445 ÷ 4no
5last digit is 0 or 5last digit 5yes
6divisible by both 2 and 3odd, digit sum 9no
8last three digits divisible by 845 ÷ 8no
9digit sum divisible by 9digits add to 9yes
10last digit is 0last digit 5no

Frequently Asked Questions

What are the factors of 45?

The factors of 45 are 1, 3, 5, 9, 15, 45.

Is 45 a prime number?

No, 45 is a composite number. Its prime factorization is 3^2 × 5.

How many factors does 45 have?

45 has 6 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 3^2 × 5 and multiply -- (2+1) × (1+1) = 6.

Is 45 even or odd?

45 is odd (2 is not a factor).

What is the sum of the factors of 45?

1 + 3 + 5 + 9 + 15 + 45 = 78. Leaving out 45 itself, the proper factors add to 33, less than 45, so 45 is a deficient number.

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