What Is the Factor of 60?

What Is the Factor of 60?

A factor of 60 is any whole number that divides 60 evenly, leaving no remainder. The complete set of positive factors is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

How to Find the Factors of 60

You can identify the factors by checking which numbers divide 60 without a remainder, or by building factor pairs that multiply to 60:

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

Stop checking at the square root of 60 (about 7.7), because every pair above that point would only repeat numbers already found.

Prime Factorization of 60

Breaking 60 down into its prime factors gives 2 × 2 × 3 × 5, or 2² × 3 × 5. This prime factorization explains why 60 has so many divisors and is useful for finding the greatest common factor or least common multiple with other numbers.

Why Factors of 60 Matter

The number 60 is highly composite, meaning it has more factors than most smaller numbers. This is one reason it appears in time (60 seconds in a minute, 60 minutes in an hour) and in geometry (the 360 degrees of a circle, which is 6 × 60). Knowing the factors helps simplify fractions, find common denominators, and solve division problems quickly.

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