What Are the Factors of 34?
A bag of 34 marbles shares evenly between just 2 friends, 17 each, and no other group size works apart from 1 and 34. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 34 are 1, 2, 17 and 34. That is four factors.
Factor Pairs of 34
Look for pairs that multiply to 34, working from the outside in.
- Start with 1 × 34.
- Try 2. Since 34 ÷ 2 = 17, write 2 × 17.
- Keep trying whole numbers until you reach 17, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 34
Prime factors show what 34 is built from. Split it and keep going until every branch is a prime.
So 34 = 2 × 17. Its prime factors are 2 and 17. Each prime appears once, so the count is (1 + 1) × (1 + 1) = 4, which matches the list.
Divisibility check for 34
A number divides by 34 when it divides by 2 and 17. Take 68: it is even and 68 ÷ 17 = 4, so 68 is a multiple of 34.
Is 34 a Prime or Composite Number?
Composite. It has four factors. The sum of all factors is 1 + 2 + 17 + 34 = 54. The factors smaller than 34 add up to 20, which is less than 34, so 34 is called a deficient number.
Real-Life Uses of the Factors of 34
- Pairs. Thirty-four shoes make 17 pairs.
- Sharing. Thirty-four marbles split evenly between 2 friends, 17 each.
- Seating. Thirty-four chairs fit in 2 rows of 17.
Common Factors of 34 With Other Numbers
The factors of 51 are 1, 3, 17 and 51, so 34 and 51 share 1 and 17. The GCF is 17, which simplifies 34/51 to 2/3.
Quick Practice
Which of these are factors of 34: 5, 17 or 7? Only 17. Now try 35 and check it with the calculator.