FactorsAbout 500
Half of 1000. 500 is 4 × 125.
Factor pairs of 500
A factor pair is two numbers that multiply to give 500: 1 × 500, 2 × 250, 4 × 125, 5 × 100, 10 × 50 and 20 × 25. Each pair is a way of arranging 500 things in equal rows, so 500 tiles can be laid out as a rectangle in 6 different shapes.
How to find the factors of 500 by hand
Divide 500 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 22, because the next number, 23, gives 23 × 23 = 529, which is more than 500: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 500? | Result |
|---|---|---|
| 1 | yes | 1 × 500 |
| 2 | yes | 2 × 250 |
| 3 | no | remainder 2 |
| 4 | yes | 4 × 125 |
| 5 | yes | 5 × 100 |
| 6 | no | remainder 2 |
| 7 | no | remainder 3 |
| 8 | no | remainder 4 |
| 9 | no | remainder 5 |
| 10 | yes | 10 × 50 |
| 11 | no | remainder 5 |
| 12 | no | remainder 8 |
| 13 | no | remainder 6 |
| 14 | no | remainder 10 |
| 15 | no | remainder 5 |
| 16 | no | remainder 4 |
| 17 | no | remainder 7 |
| 18 | no | remainder 14 |
| 19 | no | remainder 6 |
| 20 | yes | 20 × 25 |
| 21 | no | remainder 17 |
| 22 | no | remainder 16 |
The numbers that fail are 3, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21 and 22. All the others give a pair.
Prime factorisation of 500
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 500 = 2 × 2 × 5 × 5 × 5, which is written 22 × 53 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: (2 + 1) × (3 + 1) = 12. This works because a factor of 500 can use each prime anywhere from zero times up to its full power.
The 12 factors add up to 1092. Leaving out 500 itself, the rest add up to 592, which is more than 500, so 500 is an abundant number. Of its factors, 4 are odd: 1, 5, 25 and 125.
Divisibility rules applied to 500
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 5 + 0 + 0 = 5, 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: no. 500 ÷ 8 leaves remainder 4.
- By 9: no. The digits add up to 5, 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 5 and 0. Their difference is 5, which is not 0 or a multiple of 11.
HCF and LCM with 500
500 and 400. 500 = 22 × 53 and 400 = 24 × 52. 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 = 500 × 400.
500 and 625. 500 = 22 × 53 and 625 = 54. The primes they share, each with its smaller power, give the HCF: 125. Every prime with its larger power gives the LCM: 2500. By division: 625 = 500 × 1 + 125; 500 = 125 × 4 + 0, so the last divisor, 125, is the HCF. Check: 125 × 2500 = 312500 = 500 × 625.
Multiples of 500
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 500 are 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500 and 5000. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 500?
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250 and 500. There are 12 of them.
What is the prime factorisation of 500?
500 = 2 × 2 × 5 × 5 × 5.
Is 500 a perfect square?
No. 22 × 22 = 484 and 23 × 23 = 529, and 500 lies between them.
What is the greatest factor of 500 other than itself?
250. Divide 500 by its smallest prime factor, 2, to get it.