FactorsAbout 200
200 is 8 × 25. Two centuries are 200 years.
Factor pairs of 200
A factor pair is two numbers that multiply to give 200: 1 × 200, 2 × 100, 4 × 50, 5 × 40, 8 × 25 and 10 × 20. Each pair is a way of arranging 200 things in equal rows, so 200 tiles can be laid out as a rectangle in 6 different shapes.
How to find the factors of 200 by hand
Divide 200 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 14, because the next number, 15, gives 15 × 15 = 225, which is more than 200: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 200? | Result |
|---|---|---|
| 1 | yes | 1 × 200 |
| 2 | yes | 2 × 100 |
| 3 | no | remainder 2 |
| 4 | yes | 4 × 50 |
| 5 | yes | 5 × 40 |
| 6 | no | remainder 2 |
| 7 | no | remainder 4 |
| 8 | yes | 8 × 25 |
| 9 | no | remainder 2 |
| 10 | yes | 10 × 20 |
| 11 | no | remainder 2 |
| 12 | no | remainder 8 |
| 13 | no | remainder 5 |
| 14 | no | remainder 4 |
The numbers that fail are 3, 6, 7, 9, 11, 12, 13 and 14. All the others give a pair.
Prime factorisation of 200
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 200 = 2 × 2 × 2 × 5 × 5, which is written 23 × 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: (3 + 1) × (2 + 1) = 12. This works because a factor of 200 can use each prime anywhere from zero times up to its full power.
The 12 factors add up to 465. Leaving out 200 itself, the rest add up to 265, which is more than 200, so 200 is an abundant number. Of its factors, 3 are odd: 1, 5 and 25.
Divisibility rules applied to 200
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 2 + 0 + 0 = 2, 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. 200 ÷ 8 = 25.
- By 9: no. The digits add up to 2, 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 2 and 0. Their difference is 2, which is not 0 or a multiple of 11.
HCF and LCM with 200
200 and 180. 200 = 23 × 52 and 180 = 22 × 32 × 5. The primes they share, each with its smaller power, give the HCF: 20. Every prime with its larger power gives the LCM: 1800. By division: 200 = 180 × 1 + 20; 180 = 20 × 9 + 0, so the last divisor, 20, is the HCF. Check: 20 × 1800 = 36000 = 200 × 180.
200 and 216. 200 = 23 × 52 and 216 = 23 × 33. The primes they share, each with its smaller power, give the HCF: 8. Every prime with its larger power gives the LCM: 5400. By division: 216 = 200 × 1 + 16; 200 = 16 × 12 + 8; 16 = 8 × 2 + 0, so the last divisor, 8, is the HCF. Check: 8 × 5400 = 43200 = 200 × 216.
Multiples of 200
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 200 are 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800 and 2000. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 200?
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200. There are 12 of them.
What is the prime factorisation of 200?
200 = 2 × 2 × 2 × 5 × 5.
Is 200 a perfect square?
No. 14 × 14 = 196 and 15 × 15 = 225, and 200 lies between them.
What is the greatest factor of 200 other than itself?
100. Divide 200 by its smallest prime factor, 2, to get it.