FactorsAbout 100
A century, and the base of percentages. 100 is 10 × 10 and also 4 × 25. It has nine factors, an odd number because it is a perfect square.
Factor pairs of 100
A factor pair is two numbers that multiply to give 100: 1 × 100, 2 × 50, 4 × 25, 5 × 20 and 10 × 10. Each pair is a way of arranging 100 things in equal rows, so 100 tiles can be laid out as a rectangle in 5 different shapes, one of them a square of side 10.
How to find the factors of 100 by hand
Divide 100 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 10, because 10 × 10 is exactly 100: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 100? | Result |
|---|---|---|
| 1 | yes | 1 × 100 |
| 2 | yes | 2 × 50 |
| 3 | no | remainder 1 |
| 4 | yes | 4 × 25 |
| 5 | yes | 5 × 20 |
| 6 | no | remainder 4 |
| 7 | no | remainder 2 |
| 8 | no | remainder 4 |
| 9 | no | remainder 1 |
| 10 | yes | 10 × 10 |
The numbers that fail are 3, 6, 7, 8 and 9. All the others give a pair.
Prime factorisation of 100
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 100 = 2 × 2 × 5 × 5, which is written 22 × 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: (2 + 1) × (2 + 1) = 9. This works because a factor of 100 can use each prime anywhere from zero times up to its full power.
The 9 factors add up to 217. Leaving out 100 itself, the rest add up to 117, which is more than 100, so 100 is an abundant number. Of its factors, 3 are odd: 1, 5 and 25.
Divisibility rules applied to 100
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 1 + 0 + 0 = 1, 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. 100 ÷ 8 leaves remainder 4.
- By 9: no. The digits add up to 1, 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 1 and 0. Their difference is 1, which is not 0 or a multiple of 11.
HCF and LCM with 100
100 and 96. 100 = 22 × 52 and 96 = 25 × 3. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 2400. By division: 100 = 96 × 1 + 4; 96 = 4 × 24 + 0, so the last divisor, 4, is the HCF. Check: 4 × 2400 = 9600 = 100 × 96.
100 and 108. 100 = 22 × 52 and 108 = 22 × 33. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 2700. By division: 108 = 100 × 1 + 8; 100 = 8 × 12 + 4; 8 = 4 × 2 + 0, so the last divisor, 4, is the HCF. Check: 4 × 2700 = 10800 = 100 × 108.
Multiples of 100
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 100 are 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1000. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 100?
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100. There are 9 of them.
What is the prime factorisation of 100?
100 = 2 × 2 × 5 × 5.
Is 100 a perfect square?
Yes. 100 = 10 × 10, so its square root is 10.
What is the greatest factor of 100 other than itself?
50. Divide 100 by its smallest prime factor, 2, to get it.