What Are the Factors of 63?
Nine weeks is 63 days, and 63 also splits into 7 groups of 9 or 3 groups of 21. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 63 are 1, 3, 7, 9, 21 and 63. That is six factors.
Factor Pairs of 63
Look for pairs that multiply to 63, working from the outside in.
- Start with 1 × 63.
- Try 3. Since 63 ÷ 3 = 21, write 3 × 21.
- Try 7. Since 63 ÷ 7 = 9, write 7 × 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 63
Prime factors show what 63 is built from. Split it and keep going until every branch is a prime.
So 63 = 3 × 3 × 7 = 3² × 7. Its prime factors are 3 and 7. Add 1 to each exponent and multiply: (2 + 1) × (1 + 1) = 6, which matches the list.
Divisibility check for 63
A number divides by 63 when it divides by 7 and 9. Take 126: its digits add up to 9, and 126 ÷ 7 = 18, so 126 is a multiple of 63.
Is 63 a Prime or Composite Number?
Composite. It has six factors. The sum of all factors is 1 + 3 + 7 + 9 + 21 + 63 = 104. The factors smaller than 63 add up to 41, which is less than 63, so 63 is called a deficient number.
Real-Life Uses of the Factors of 63
- Weeks. Sixty-three days is exactly 9 weeks.
- Rows. Sixty-three seats fit in 7 rows of 9.
- Sharing. Sixty-three apples share evenly between 3, 7, 9 or 21 people.
Common Factors of 63 With Other Numbers
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84, so 63 and 84 share 1, 3, 7 and 21. The GCF is 21, which simplifies 63/84 to 3/4.
Quick Practice
Which of these are factors of 63: 5, 7 or 8? Only 7. Now try 64 and check it with the calculator.