What are the factor pairs of 42?

The pairs are (1, 42), (2, 21), (3, 14) and (6, 7). Each pair multiplies to 42.

What is the prime factorization of 42?

42 = 2 × 3 × 7. All three primes are different and each appears once.

What is the greatest common factor of 42 and 56?

The GCF of 42 and 56 is 14. The common factors are 1, 2, 7 and 14, and 14 is the largest.

Factors of 42 - Factor Pairs & Prime Factorization

Q: What are the factors of 42?

The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. That is eight factors.

What Are the Factors of 42?

Picture 42 marbles. You can set them out as 1 row of 42, 2 rows of 21, 3 rows of 14 or 6 rows of 7, and every one of those neat layouts is a factor. A factor is a whole number that divides another number exactly, with no remainder.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. That is eight factors.

Factor Pairs of 42

Look for pairs that multiply to 42, from the outside in.

Handwritten notebook page titled Factors of 42 showing 1 × 42, 2 × 21, 3 × 14 and 6 × 7 all equal to 42, with the eight factors 1, 2, 3, 6, 7, 14, 21 and 42 circled in red and the note 8 factors — The four pairs of 42, with every factor circled.

Start with 1 × 42.
Try 2. Since 42 ÷ 2 = 21, write 2 × 21.
Try 3. Since 42 ÷ 3 = 14, write 3 × 14.
Try 4 and 5. Neither divides 42, so skip them.
Try 6. Since 42 ÷ 6 = 7, write 6 × 7. The next number, 7, is already used, so you are done.

Prime Factorization of 42

Prime factors show what 42 is built from. Split it and keep going until every branch is prime.

Handwritten factor tree of 42 splitting into 6 and 7, then 6 into 2 and 3, with the primes 2, 3 and 7 circled in red and 42 = 2 × 3 × 7 written below — Factor tree of 42. The circled primes are 2, 3 and 7.

So 42 = 2 × 3 × 7. Three different primes, each used once. Add 1 to each exponent and multiply: (1 + 1) × (1 + 1) × (1 + 1) = 8, which matches the list.

Divisibility check for 42

A number divides by 42 when it divides by 2, 3 and 7 together. Take 126: it is even, its digits add up to 9 (a multiple of 3) and 126 ÷ 7 = 18. So 126 is a multiple of 42.

Is 42 a Prime or Composite Number?

Composite. It has eight factors. The sum of all factors is 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 = 96. Because 42 is the product of exactly three different primes, it is also called a sphenic number. It is a pronic number too, since 42 = 6 × 7, two numbers in a row.

Real-Life Uses of the Factors of 42

Weeks. Forty-two days is exactly 6 weeks, because 6 × 7 = 42.
Sharing. Forty-two cookies share evenly between 2, 3, 6, 7, 14 or 21 people.
Pop culture. 42 is the famous answer to life, the universe and everything in The Hitchhiker's Guide to the Galaxy.

Common Factors of 42 With Other Numbers

The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56, so 42 and 56 share 1, 2, 7 and 14. The GCF is 14, which simplifies 42/56 to 3/4.

Quick Practice

Which of these are factors of 42: 6, 8 or 14? That is 6 and 14. Now try 84 and check it with the calculator.

Factors of 42