FactorsAbout 56
56 is 7 × 8, the times table fact children miss most. It is also 2 × 2 × 2 × 7, and eight weeks contain 56 days.
Factor pairs of 56
A factor pair is two numbers that multiply to give 56: 1 × 56, 2 × 28, 4 × 14 and 7 × 8. Each pair is a way of arranging 56 things in equal rows, so 56 tiles can be laid out as a rectangle in 4 different shapes.
How to find the factors of 56 by hand
Divide 56 by 1, 2, 3 and so on. Each time the division is exact, you have found two factors at once: the divisor and the answer. You can stop at 7, because the next number, 8, gives 8 × 8 = 64, which is more than 56: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 56? | Result |
|---|---|---|
| 1 | yes | 1 × 56 |
| 2 | yes | 2 × 28 |
| 3 | no | remainder 2 |
| 4 | yes | 4 × 14 |
| 5 | no | remainder 1 |
| 6 | no | remainder 2 |
| 7 | yes | 7 × 8 |
The numbers that fail are 3, 5 and 6. All the others give a pair.
Prime factorisation of 56
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 56 = 2 × 2 × 2 × 7, which is written 23 × 7 with powers. Its prime factors are 2 and 7.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (3 + 1) × (1 + 1) = 8. This works because a factor of 56 can use each prime anywhere from zero times up to its full power.
The 8 factors add up to 120. Leaving out 56 itself, the rest add up to 64, which is more than 56, so 56 is an abundant number. Of its factors, 2 are odd: 1 and 7.
Divisibility rules applied to 56
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 6, which is even.
- By 3: no. The digits add up to 5 + 6 = 11, which is not a multiple of 3.
- By 4: yes. The last two digits make 56, and 56 ÷ 4 = 14.
- By 5: no. The last digit is 6, not 0 or 5.
- By 6: no. A number divides by 6 when it divides by both 2 and 3. Here the test for 3 fails.
- By 8: yes. 56 ÷ 8 = 7.
- By 9: no. The digits add up to 11, which is not a multiple of 9.
- By 10: no. The last digit is not 0.
- By 11: no. Adding alternate digits from the right gives 6 and 5. Their difference is 1, which is not 0 or a multiple of 11.
HCF and LCM with 56
56 and 54. 56 = 23 × 7 and 54 = 2 × 33. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 1512. By division: 56 = 54 × 1 + 2; 54 = 2 × 27 + 0, so the last divisor, 2, is the HCF. Check: 2 × 1512 = 3024 = 56 × 54.
56 and 60. 56 = 23 × 7 and 60 = 22 × 3 × 5. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 840. By division: 60 = 56 × 1 + 4; 56 = 4 × 14 + 0, so the last divisor, 4, is the HCF. Check: 4 × 840 = 3360 = 56 × 60.
Multiples of 56
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 56 are 56, 112, 168, 224, 280, 336, 392, 448, 504 and 560. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 56?
The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56. There are 8 of them.
What is the prime factorisation of 56?
56 = 2 × 2 × 2 × 7.
Is 56 a perfect square?
No. 7 × 7 = 49 and 8 × 8 = 64, and 56 lies between them.
What is the greatest factor of 56 other than itself?
28. Divide 56 by its smallest prime factor, 2, to get it.