Study Guides/Maths/Factors of 60
Study Guide · Maths

Factors of 60 and Prime Factorization

The number 60 is a very special number in mathematics. It is known as a 'highly composite number' because it has a huge number of factors for its size. This is exactly why ancient civilizations chose 60 to divide time (60 seconds, 60 minutes) and circles (360 degrees).

Question (Click to Flip)

How many factors does 60 have?

Answer

The number 60 has exactly 12 positive factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

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Key Facts

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Total number of factors: 12.

Prime factors: 2, 3, 5.

Type: Highly Composite Number.

What are the Factors of 60?

Let's find all the number pairs that multiply to give 60:

  • 1 × 60 = 60
  • 2 × 30 = 60
  • 3 × 20 = 60
  • 4 × 15 = 60
  • 5 × 12 = 60
  • 6 × 10 = 60

Listing them all out, the factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Prime Factorization of 60

Let's break 60 down into prime numbers using a factor tree:

  • 60 = 2 × 30
  • 30 = 2 × 15
  • 15 = 3 × 5

Prime Factorization of 60 = 2 × 2 × 3 × 5 (or 2² × 3 × 5).

Why is 60 so useful?

Because 60 has 12 factors, it can be easily divided into halves (30), thirds (20), quarters (15), fifths (12), and sixths (10) without creating decimals. This makes it perfect for fractions and timekeeping!

Questions and Answers

How many factors does 60 have?+

The number 60 has exactly 12 positive factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

What is the prime factorization of 60?+

The prime factorization of 60 is 2 × 2 × 3 × 5 (or 2² × 3 × 5).

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