What Are the Factors of 28?
February in a normal year has 28 days, which is exactly 4 weeks of 7 days or 2 fortnights 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 28 are 1, 2, 4, 7, 14 and 28. That is six factors.
Factor Pairs of 28
Look for pairs that multiply to 28, working from the outside in.
- Start with 1 × 28.
- Try 2. Since 28 ÷ 2 = 14, write 2 × 14.
- Try 4. Since 28 ÷ 4 = 7, write 4 × 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 28
Prime factors show what 28 is built from. Split it and keep going until every branch is a prime.
So 28 = 2 × 2 × 7 = 2² × 7. Its prime factors are 2 and 7. Add 1 to each exponent and multiply: (2 + 1) × (1 + 1) = 6, which matches the list.
Divisibility check for 28
A number divides by 28 when it divides by 4 and 7. Take 84: its last two digits give 84 ÷ 4 = 21, and 84 ÷ 7 = 12, so 84 is a multiple of 28.
Is 28 a Prime or Composite Number?
Composite. It has six factors. The sum of all factors is 1 + 2 + 4 + 7 + 14 + 28 = 56. The factors smaller than 28 add up to exactly 28, so 28 is a perfect number.
Real-Life Uses of the Factors of 28
- February. Twenty-eight days make exactly 4 weeks.
- Shelves. Twenty-eight books fit on 4 shelves of 7 or 2 shelves of 14.
- Perfect number. Because its smaller factors add up to 28, mathematicians call it a perfect number.
Common Factors of 28 With Other Numbers
The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42, so 28 and 42 share 1, 2, 7 and 14. The GCF is 14, which simplifies 28/42 to 2/3.
Quick Practice
Which of these are factors of 28: 5, 7 or 8? Only 7. Now try 30 and check it with the calculator.