FactorsAbout 20
A score is an old word for 20. Twenty 5-rupee coins make ₹100, and twenty has six factors.
Factor pairs of 20
A factor pair is two numbers that multiply to give 20: 1 × 20, 2 × 10 and 4 × 5. Each pair is a way of arranging 20 things in equal rows, so 20 tiles can be laid out as a rectangle in 3 different shapes.
How to find the factors of 20 by hand
Divide 20 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 4, because the next number, 5, gives 5 × 5 = 25, which is more than 20: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 20? | Result |
|---|---|---|
| 1 | yes | 1 × 20 |
| 2 | yes | 2 × 10 |
| 3 | no | remainder 2 |
| 4 | yes | 4 × 5 |
The only number that fails is 3. All the others give a pair.
Prime factorisation of 20
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 20 = 2 × 2 × 5, which is written 22 × 5 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) × (1 + 1) = 6. This works because a factor of 20 can use each prime anywhere from zero times up to its full power.
The 6 factors add up to 42. Leaving out 20 itself, the rest add up to 22, which is more than 20, so 20 is an abundant number. Of its factors, 2 are odd: 1 and 5.
Divisibility rules applied to 20
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 = 2, which is not a multiple of 3.
- By 4: yes. The last two digits make 20, and 20 ÷ 4 = 5.
- 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. 20 ÷ 8 leaves remainder 4.
- 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 0 and 2. Their difference is 2, which is not 0 or a multiple of 11.
HCF and LCM with 20
20 and 18. 20 = 22 × 5 and 18 = 2 × 32. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 180. By division: 20 = 18 × 1 + 2; 18 = 2 × 9 + 0, so the last divisor, 2, is the HCF. Check: 2 × 180 = 360 = 20 × 18.
20 and 24. 20 = 22 × 5 and 24 = 23 × 3. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 120. By division: 24 = 20 × 1 + 4; 20 = 4 × 5 + 0, so the last divisor, 4, is the HCF. Check: 4 × 120 = 480 = 20 × 24.
Multiples of 20
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, 180 and 200. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 20?
The factors of 20 are 1, 2, 4, 5, 10 and 20. There are 6 of them.
What is the prime factorisation of 20?
20 = 2 × 2 × 5.
Is 20 a perfect square?
No. 4 × 4 = 16 and 5 × 5 = 25, and 20 lies between them.
What is the greatest factor of 20 other than itself?
10. Divide 20 by its smallest prime factor, 2, to get it.