Factors of 56
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. 56 is a composite number with 8 factors. Prime factorisation: 2^3 × 7.
All 8 factors of 56
1, 2, 4, 7, 8, 14, 28, 56
A factor divides 56 exactly, with no remainder. Every factor has a partner: the pairs below multiply to 56. The negative factors are -1, -2, -4, -7, -8, -14, -28, -56, because a negative times a negative is positive.
Factor pairs of 56
| Pair | Product |
|---|---|
| 1 × 56 | 56 |
| 2 × 28 | 56 |
| 4 × 14 | 56 |
| 7 × 8 | 56 |
Stop at the square root (7): every pair after that is one you already have, the other way round.
Prime factorisation of 56: 2^3 × 7
| Divide | by the smallest prime | Result |
|---|---|---|
| 56 | 2 | 28 |
| 28 | 2 | 14 |
| 14 | 2 | 7 |
| 7 | 7 | 1 |
So 56 = 23 × 7, that is 2 × 2 × 2 × 7.
The number of factors comes from the exponents: (3 + 1) × (1 + 1) = 8.
How to find the factors of 56
- Start with 1 and 56: every number has those two.
- Test 2, 3, 4, … up to the square root of 56, which is about 7.
- Each time a number divides exactly, write it down with its partner (the quotient).
- Use the divisibility rules to skip work: by 2 yes (the last digit is even); by 3 no (the digit sum is 11); by 5 no (the last digit is 6).
- Put the list in order: 1, 2, 4, 7, 8, 14, ….
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. List the factors of 57.
Answer: 1, 3, 19, 57
2. Write the prime factorisation of 112.
Answer: 2^4 × 7
3. How many factors does 56 have?
Answer: 8
4. What is the largest factor of 56 other than itself?
Answer: 28
5. Is 58 prime or composite?
Answer: composite
📚 The class this belongs to
Factors are taught in Grade 4 and 5 in the US, Year 5 and 6 in the UK, Class 4 to 6 in CBSE (NCERT Class 6, Playing with Numbers) and Year 5 and 6 in Australia.
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