FactorsAbout 42
42 is 2 × 3 × 7, the product of three different primes. Six weeks contain 42 days.
Factor pairs of 42
A factor pair is two numbers that multiply to give 42: 1 × 42, 2 × 21, 3 × 14 and 6 × 7. Each pair is a way of arranging 42 things in equal rows, so 42 tiles can be laid out as a rectangle in 4 different shapes.
How to find the factors of 42 by hand
Divide 42 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 42: any larger factor has already turned up as the partner of a smaller one.
| Try | Divides 42? | Result |
|---|---|---|
| 1 | yes | 1 × 42 |
| 2 | yes | 2 × 21 |
| 3 | yes | 3 × 14 |
| 4 | no | remainder 2 |
| 5 | no | remainder 2 |
| 6 | yes | 6 × 7 |
The numbers that fail are 4 and 5. All the others give a pair.
Prime factorisation of 42
Divide by the smallest prime that goes in exactly, and repeat with the answer until you reach 1.
Reading down the left side: 42 = 2 × 3 × 7. Its prime factors are 2, 3 and 7.
Counting the factors without listing them
Add 1 to each power in the prime factorisation and multiply the results: (1 + 1) × (1 + 1) × (1 + 1) = 8. This works because a factor of 42 can use each prime anywhere from zero times up to its full power.
The 8 factors add up to 96. Leaving out 42 itself, the rest add up to 54, which is more than 42, so 42 is an abundant number. Of its factors, 4 are odd: 1, 3, 7 and 21.
Divisibility rules applied to 42
The quick tests agree with the factor list above.
- By 2: yes. The last digit is 2, which is even.
- By 3: yes. The digits add up to 4 + 2 = 6, which is a multiple of 3.
- By 4: no. The last two digits make 42, and 42 ÷ 4 leaves remainder 2.
- By 5: no. The last digit is 2, not 0 or 5.
- By 6: yes. A number divides by 6 when it divides by both 2 and 3. Here both tests pass.
- By 8: no. 42 ÷ 8 leaves remainder 2.
- By 9: no. The digits add up to 6, which is not a multiple of 9.
- By 10: no. The last digit is not 0.
- By 11: no. Adding alternate digits from the right gives 2 and 4. Their difference is 2, which is not 0 or a multiple of 11.
HCF and LCM with 42
42 and 40. 42 = 2 × 3 × 7 and 40 = 23 × 5. 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 = 42 × 40.
42 and 45. 42 = 2 × 3 × 7 and 45 = 32 × 5. The primes they share, each with its smaller power, give the HCF: 3. Every prime with its larger power gives the LCM: 630. By division: 45 = 42 × 1 + 3; 42 = 3 × 14 + 0, so the last divisor, 3, is the HCF. Check: 3 × 630 = 1890 = 42 × 45.
Multiples of 42
Factors divide a number. Multiples are what you get by multiplying it. The first ten multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378 and 420. A number has a fixed count of factors but endless multiples.
Common questions
What are the factors of 42?
The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. There are 8 of them.
What is the prime factorisation of 42?
42 = 2 × 3 × 7.
Is 42 a perfect square?
No. 6 × 6 = 36 and 7 × 7 = 49, and 42 lies between them.
What is the greatest factor of 42 other than itself?
21. Divide 42 by its smallest prime factor, 2, to get it.