What Are the Factors of 33?
A playlist of 33 songs can only be split evenly into 3 groups of 11 or 11 groups of 3. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 33 are 1, 3, 11 and 33. That is four factors.
Factor Pairs of 33
Look for pairs that multiply to 33, working from the outside in.
- Start with 1 × 33.
- Try 3. Since 33 ÷ 3 = 11, write 3 × 11.
- Keep trying whole numbers until you reach 11, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 33
Prime factors show what 33 is built from. Split it and keep going until every branch is a prime.
So 33 = 3 × 11. Its prime factors are 3 and 11. Each prime appears once, so the count is (1 + 1) × (1 + 1) = 4, which matches the list.
Divisibility check for 33
A number divides by 33 when it divides by 3 and 11. Take 99: its digits add up to 18, a multiple of 3, and 9 − 9 = 0 so it divides by 11. So 99 is a multiple of 33.
Is 33 a Prime or Composite Number?
Composite. It has four factors. The sum of all factors is 1 + 3 + 11 + 33 = 48. The factors smaller than 33 add up to 15, which is less than 33, so 33 is called a deficient number.
Real-Life Uses of the Factors of 33
- Playlists. Thirty-three songs make 3 sets of 11.
- Rows. Thirty-three seats fit in 3 rows of 11.
- Sharing. Thirty-three sweets share evenly only between 3 or 11 people.
Common Factors of 33 With Other Numbers
The factors of 44 are 1, 2, 4, 11, 22 and 44, so 33 and 44 share 1 and 11. The GCF is 11, which simplifies 33/44 to 3/4.
Quick Practice
Which of these are factors of 33: 5, 11 or 7? Only 11. Now try 34 and check it with the calculator.