What Are the Factors of 45?
A 45-minute lesson splits into 3 blocks of 15, 5 blocks of 9 or 9 blocks of 5. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 45 are 1, 3, 5, 9, 15 and 45. That is six factors.
Factor Pairs of 45
Look for pairs that multiply to 45, working from the outside in.
- Start with 1 × 45.
- Try 3. Since 45 ÷ 3 = 15, write 3 × 15.
- Try 5. Since 45 ÷ 5 = 9, write 5 × 9.
- Keep trying whole numbers until you reach 9, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 45
Prime factors show what 45 is built from. Split it and keep going until every branch is a prime.
So 45 = 3 × 3 × 5 = 3² × 5. Its prime factors are 3 and 5. Add 1 to each exponent and multiply: (2 + 1) × (1 + 1) = 6, which matches the list.
Divisibility check for 45
A number divides by 45 when it divides by 5 and 9. Take 135: it ends in 5 and its digits add up to 9, so 135 is a multiple of 45.
Is 45 a Prime or Composite Number?
Composite. It has six factors. The sum of all factors is 1 + 3 + 5 + 9 + 15 + 45 = 78. The factors smaller than 45 add up to 33, which is less than 45, so 45 is called a deficient number.
Real-Life Uses of the Factors of 45
- Lessons. A 45-minute lesson splits into 3 blocks of 15.
- Angles. Forty-five degrees is half of a right angle.
- Rows. Forty-five chairs fit in 5 rows of 9.
Common Factors of 45 With Other Numbers
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, so 45 and 60 share 1, 3, 5 and 15. The GCF is 15, which simplifies 45/60 to 3/4.
Quick Practice
Which of these are factors of 45: 6, 5 or 8? Only 5. Now try 54 and check it with the calculator.