FactorsAbout 40
40 is 2 × 2 × 2 × 5. Four tens, five eights and two twenties all make forty.
Factor pairs of 40
A factor pair is two numbers that multiply to give 40: 1 × 40, 2 × 20, 4 × 10 and 5 × 8. Each pair is a way of arranging 40 things in equal rows, so 40 tiles can be laid out as a rectangle in 4 different shapes.
How to find the factors of 40 by hand
Divide 40 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 6, because the next number, 7, gives 7 × 7 = 49, which is more than 40: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 40? | Result |
|---|---|---|
| 1 | yes | 1 × 40 |
| 2 | yes | 2 × 20 |
| 3 | no | remainder 1 |
| 4 | yes | 4 × 10 |
| 5 | yes | 5 × 8 |
| 6 | no | remainder 4 |
The numbers that fail are 3 and 6. All the others give a pair.
Prime factorisation of 40
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 40 = 2 × 2 × 2 × 5, which is written 23 × 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: (3 + 1) × (1 + 1) = 8. This works because a factor of 40 can use each prime anywhere from zero times up to its full power.
The 8 factors add up to 90. Leaving out 40 itself, the rest add up to 50, which is more than 40, so 40 is an abundant number. Of its factors, 2 are odd: 1 and 5.
Divisibility rules applied to 40
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 = 4, which is not a multiple of 3.
- By 4: yes. The last two digits make 40, and 40 ÷ 4 = 10.
- 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. 40 ÷ 8 = 5.
- 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 0 and 4. Their difference is 4, which is not 0 or a multiple of 11.
HCF and LCM with 40
40 and 36. 40 = 23 × 5 and 36 = 22 × 32. The primes they share, each with its smaller power, give the HCF: 4. Every prime with its larger power gives the LCM: 360. By division: 40 = 36 × 1 + 4; 36 = 4 × 9 + 0, so the last divisor, 4, is the HCF. Check: 4 × 360 = 1440 = 40 × 36.
40 and 42. 40 = 23 × 5 and 42 = 2 × 3 × 7. The primes they share, each with its smaller power, give the HCF: 2. Every prime with its larger power gives the LCM: 840. By division: 42 = 40 × 1 + 2; 40 = 2 × 20 + 0, so the last divisor, 2, is the HCF. Check: 2 × 840 = 1680 = 40 × 42.
Multiples of 40
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 40 are 40, 80, 120, 160, 200, 240, 280, 320, 360 and 400. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 40?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40. There are 8 of them.
What is the prime factorisation of 40?
40 = 2 × 2 × 2 × 5.
Is 40 a perfect square?
No. 6 × 6 = 36 and 7 × 7 = 49, and 40 lies between them.
What is the greatest factor of 40 other than itself?
20. Divide 40 by its smallest prime factor, 2, to get it.