What are the factor pairs of 180?

The pairs are (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18) and (12, 15). Each pair multiplies to 180.

What is the greatest common factor of 180 and 240?

The GCF of 180 and 240 is 60. The common factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, and 60 is the largest.

Factors of 180 - Factor Pairs & Prime Factorization

Q: What are the factors of 180?

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180. That is eighteen factors, and each one divides 180 exactly.

Q: What is the prime factorization of 180?

180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5. Its prime factors are 2, 3 and 5.

What Are the Factors of 180?

A straight angle is 180 degrees and the three angles of any triangle add up to 180, so this number is everywhere in geometry. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180. That is eighteen factors.

Factor Pairs of 180

Look for pairs that multiply to 180, working from the outside in.

Handwritten notebook page titled Factors of 180 showing 1 × 180, 2 × 90, 3 × 60, 4 × 45, 5 × 36, 6 × 30, 9 × 20, 10 × 18, 12 × 15 all equal to 180, with the eighteen factors 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180 circled in red and the note 18 factors — The 9 pairs of 180, with every factor circled.

Start with 1 × 180.
Try 2. Since 180 ÷ 2 = 90, write 2 × 90.
Try 3. Since 180 ÷ 3 = 60, write 3 × 60.
Try 4. Since 180 ÷ 4 = 45, write 4 × 45.
Try 5. Since 180 ÷ 5 = 36, write 5 × 36.
Try 6. Since 180 ÷ 6 = 30, write 6 × 30.
Try 9. Since 180 ÷ 9 = 20, write 9 × 20.
Try 10. Since 180 ÷ 10 = 18, write 10 × 18.
Try 12. Since 180 ÷ 12 = 15, write 12 × 15.
Keep trying whole numbers until you reach 15, which is already in your list. Every factor is now found, so you are done.

Prime Factorization of 180

Prime factors show what 180 is built from. Split it and keep going until every branch is a prime.

Handwritten factor tree of 180 splitting down to the circled primes 2, 2, 3, 3 and 5, with 180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5 written below — Factor tree of 180. The circled primes are 2, 2, 3, 3 and 5.

So 180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5. Its prime factors are 2, 3 and 5. Add 1 to each exponent and multiply: (2 + 1) × (2 + 1) × (1 + 1) = 18, which matches the list.

Divisibility check for 180

A number divides by 180 when it divides by 4, 9 and 5. Take 540: its last two digits give 40 ÷ 4 = 10, its digits add up to 9, and it ends in 0, so 540 is a multiple of 180.

Is 180 a Prime or Composite Number?

Composite. It has eighteen factors. The sum of all factors is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180 = 546. The factors smaller than 180 add up to 366, which is more than 180, so 180 is called an abundant number.

Real-Life Uses of the Factors of 180

Triangles. The three angles of any triangle add up to 180 degrees.
Straight lines. A straight angle measures 180 degrees.
Groups. With eighteen factors, 180 students can form equal groups of 2, 3, 4, 5, 6, 9, 10, 12 and more with nobody left out.

Common Factors of 180 With Other Numbers

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240, so 180 and 240 share 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. The GCF is 60, which simplifies 180/240 to 3/4.

Quick Practice

Which of these are factors of 180: 7, 5 or 11? Only 5. Now try 18 and check it with the calculator.

Factors of 180