FactorsAbout 400
400 is 20 × 20, a perfect square. Four centuries are 400 years.
Factor pairs of 400
A factor pair is two numbers that multiply to give 400: 1 × 400, 2 × 200, 4 × 100, 5 × 80, 8 × 50, 10 × 40, 16 × 25 and 20 × 20. Each pair is a way of arranging 400 things in equal rows, so 400 tiles can be laid out as a rectangle in 8 different shapes, one of them a square of side 20.
How to find the factors of 400 by hand
Divide 400 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 20, because 20 × 20 is exactly 400: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 400? | Result |
|---|---|---|
| 1 | yes | 1 × 400 |
| 2 | yes | 2 × 200 |
| 3 | no | remainder 1 |
| 4 | yes | 4 × 100 |
| 5 | yes | 5 × 80 |
| 6 | no | remainder 4 |
| 7 | no | remainder 1 |
| 8 | yes | 8 × 50 |
| 9 | no | remainder 4 |
| 10 | yes | 10 × 40 |
| 11 | no | remainder 4 |
| 12 | no | remainder 4 |
| 13 | no | remainder 10 |
| 14 | no | remainder 8 |
| 15 | no | remainder 10 |
| 16 | yes | 16 × 25 |
| 17 | no | remainder 9 |
| 18 | no | remainder 4 |
| 19 | no | remainder 1 |
| 20 | yes | 20 × 20 |
The numbers that fail are 3, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18 and 19. All the others give a pair.
Prime factorisation of 400
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 400 = 2 × 2 × 2 × 2 × 5 × 5, which is written 24 × 52 with powers. Its prime factors are 2 and 5.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (4 + 1) × (2 + 1) = 15. This works because a factor of 400 can use each prime anywhere from zero times up to its full power.
The 15 factors add up to 961. Leaving out 400 itself, the rest add up to 561, which is more than 400, so 400 is an abundant number. Of its factors, 3 are odd: 1, 5 and 25.
Divisibility rules applied to 400
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 0, which is even.
- By 3: no. The digits add up to 4 + 0 + 0 = 4, which is not a multiple of 3.
- By 4: yes. The last two digits make 0, and 0 ÷ 4 = 0.
- By 5: yes. The last digit is 0.
- 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. 400 ÷ 8 = 50.
- By 9: no. The digits add up to 4, which is not a multiple of 9.
- By 10: yes. The last digit is 0.
- By 11: no. Adding alternate digits from the right gives 4 and 0. Their difference is 4, which is not 0 or a multiple of 11.
HCF and LCM with 400
400 and 360. 400 = 24 × 52 and 360 = 23 × 32 × 5. The primes they share, each with its smaller power, give the HCF: 40. Every prime with its larger power gives the LCM: 3600. By division: 400 = 360 × 1 + 40; 360 = 40 × 9 + 0, so the last divisor, 40, is the HCF. Check: 40 × 3600 = 144000 = 400 × 360.
400 and 500. 400 = 24 × 52 and 500 = 22 × 53. The primes they share, each with its smaller power, give the HCF: 100. Every prime with its larger power gives the LCM: 2000. By division: 500 = 400 × 1 + 100; 400 = 100 × 4 + 0, so the last divisor, 100, is the HCF. Check: 100 × 2000 = 200000 = 400 × 500.
Multiples of 400
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 400 are 400, 800, 1200, 1600, 2000, 2400, 2800, 3200, 3600 and 4000. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 400?
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400. There are 15 of them.
What is the prime factorisation of 400?
400 = 2 × 2 × 2 × 2 × 5 × 5.
Is 400 a perfect square?
Yes. 400 = 20 × 20, so its square root is 20.
What is the greatest factor of 400 other than itself?
200. Divide 400 by its smallest prime factor, 2, to get it.