What Are the Factors of 35?
A shelf of 35 books can be arranged in 5 rows of 7 or 7 rows 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 35 are 1, 5, 7 and 35. That is four factors.
Factor Pairs of 35
Look for pairs that multiply to 35, working from the outside in.
- Start with 1 × 35.
- Try 5. Since 35 ÷ 5 = 7, write 5 × 7.
- Keep trying whole numbers until you reach 7, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 35
Prime factors show what 35 is built from. Split it and keep going until every branch is a prime.
So 35 = 5 × 7. Its prime factors are 5 and 7. Each prime appears once, so the count is (1 + 1) × (1 + 1) = 4, which matches the list.
Divisibility check for 35
A number divides by 35 when it divides by 5 and 7. Take 105: it ends in 5, and 105 ÷ 7 = 15, so 105 is a multiple of 35.
Is 35 a Prime or Composite Number?
Composite. It has four factors. The sum of all factors is 1 + 5 + 7 + 35 = 48. The factors smaller than 35 add up to 13, which is less than 35, so 35 is called a deficient number.
Real-Life Uses of the Factors of 35
- Shelves. Thirty-five books fill 5 shelves of 7.
- Weeks. Thirty-five days is exactly 5 weeks.
- Rows. Thirty-five plants fit in 7 rows of 5.
Common Factors of 35 With Other Numbers
The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56, so 35 and 56 share 1 and 7. The GCF is 7, which simplifies 35/56 to 5/8.
Quick Practice
Which of these are factors of 35: 6, 5 or 9? Only 5. Now try 39 and check it with the calculator.