What Are the Factors of 70?
Seventy minutes splits into 7 blocks of 10, 10 blocks of 7 or 5 blocks of 14. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70. That is eight factors.
Factor Pairs of 70
Look for pairs that multiply to 70, working from the outside in.
- Start with 1 × 70.
- Try 2. Since 70 ÷ 2 = 35, write 2 × 35.
- Try 5. Since 70 ÷ 5 = 14, write 5 × 14.
- Try 7. Since 70 ÷ 7 = 10, write 7 × 10.
- Keep trying whole numbers until you reach 10, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 70
Prime factors show what 70 is built from. Split it and keep going until every branch is a prime.
So 70 = 2 × 5 × 7. Its prime factors are 2, 5 and 7. Each prime appears once, so the count is (1 + 1) × (1 + 1) × (1 + 1) = 8, which matches the list.
Divisibility check for 70
A number divides by 70 when it divides by 7 and 10. Take 210: it ends in 0, and 210 ÷ 7 = 30, so 210 is a multiple of 70.
Is 70 a Prime or Composite Number?
Composite. It has eight factors. The sum of all factors is 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 = 144. The factors smaller than 70 add up to 74, which is more than 70, so 70 is called an abundant number.
Real-Life Uses of the Factors of 70
- Time. Seventy minutes is 7 blocks of 10.
- Rows. Seventy seats fit in 5 rows of 14 or 7 rows of 10.
- Sharing. Seventy sweets share evenly between 2, 5, 7 or 10 people.
Common Factors of 70 With Other Numbers
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84, so 70 and 84 share 1, 2, 7 and 14. The GCF is 14, which simplifies 70/84 to 5/6.
Quick Practice
Which of these are factors of 70: 6, 5 or 9? Only 5. Now try 72 and check it with the calculator.