What are the factor pairs of 90?

The pairs are (1, 90), (2, 45), (3, 30), (5, 18), (6, 15) and (9, 10). Each pair multiplies to 90.

What is the greatest common factor of 90 and 120?

The GCF of 90 and 120 is 30. The common factors are 1, 2, 3, 5, 6, 10, 15 and 30, and 30 is the largest.

Factors of 90 - Factor Pairs & Prime Factorization

Q: What are the factors of 90?

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90. That is twelve factors, and each one divides 90 exactly.

Q: What is the prime factorization of 90?

90 = 2 × 3 × 3 × 5 = 2 × 3² × 5. Its prime factors are 2, 3 and 5.

What Are the Factors of 90?

A right angle measures 90 degrees, and 90 splits into 2 halves of 45, 3 parts of 30 or 5 parts of 18. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90. That is twelve factors.

Factor Pairs of 90

Look for pairs that multiply to 90, working from the outside in.

Handwritten notebook page titled Factors of 90 showing 1 × 90, 2 × 45, 3 × 30, 5 × 18, 6 × 15, 9 × 10 all equal to 90, with the twelve factors 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90 circled in red and the note 12 factors — The 6 pairs of 90, with every factor circled.

Start with 1 × 90.
Try 2. Since 90 ÷ 2 = 45, write 2 × 45.
Try 3. Since 90 ÷ 3 = 30, write 3 × 30.
Try 5. Since 90 ÷ 5 = 18, write 5 × 18.
Try 6. Since 90 ÷ 6 = 15, write 6 × 15.
Try 9. Since 90 ÷ 9 = 10, write 9 × 10.
Keep trying whole numbers until you reach 10, which is already in your list. Every factor is now found, so you are done.

Prime Factorization of 90

Prime factors show what 90 is built from. Split it and keep going until every branch is a prime.

Handwritten factor tree of 90 splitting down to the circled primes 2, 3, 3 and 5, with 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5 written below — Factor tree of 90. The circled primes are 2, 3, 3 and 5.

So 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5. Its prime factors are 2, 3 and 5. Add 1 to each exponent and multiply: (1 + 1) × (2 + 1) × (1 + 1) = 12, which matches the list.

Divisibility check for 90

A number divides by 90 when it divides by 9 and 10. Take 270: it ends in 0 and its digits add up to 9, so 270 is a multiple of 90.

Is 90 a Prime or Composite Number?

Composite. It has twelve factors. The sum of all factors is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234. The factors smaller than 90 add up to 144, which is more than 90, so 90 is called an abundant number.

Real-Life Uses of the Factors of 90

Right angles. A right angle is 90 degrees, so 90 appears in every square corner.
Football. A football match lasts 90 minutes, which is 3 blocks of 30.
Sharing. Ninety stickers share evenly between 2, 3, 5, 6, 9 or 10 people.

Common Factors of 90 With Other Numbers

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120, so 90 and 120 share 1, 2, 3, 5, 6, 10, 15 and 30. The GCF is 30, which simplifies 90/120 to 3/4.

Quick Practice

Which of these are factors of 90: 7, 5 or 11? Only 5. Now try 96 and check it with the calculator.

Factors of 90