Find all factors of a number, prime factorization, factor pairs, and more. Understand the divisibility properties of any positive integer.
Number of Factors
12
Composite number
60 is a composite number
Enter a positive integer to find all its factors.
Highlighted factors are prime numbers
Each pair of factors multiplies to give 60:
60=2^2 × 3 × 5
Prime factors: 2, 3, 5
Type
Composite
Factor Count
12
Sum of Factors
168
Perfect Square?
No
Sum of proper divisors (excluding 60)
108
60 is an abundant number (less than sum of proper divisors)
Green indicates 60 is divisible by that number.
Number of Factors
12
Composite number
60 is a composite number
To find all factors of a number, start from 1 and check each integer up to the square root. If a number divides evenly, both it and the quotient are factors. For example, factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factor pairs multiply to give the original number: 1x36, 2x18, 3x12, 4x9, 6x6.
A factor (or divisor) is a number that divides evenly into another number with no remainder. Finding factors is fundamental to understanding number theory, simplifying fractions, finding GCF and LCM, and solving various mathematical problems. Factors always come in pairs that multiply to give the original number.
To find all factors of a number, start from 1 and check each integer up to the square root. If a number divides evenly, both it and the quotient are factors. For example, factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factor pairs multiply to give the original number: 1x36, 2x18, 3x12, 4x9, 6x6.
A factor is a number that divides evenly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 with no remainder.
Prime factors are factors that are prime numbers (only divisible by 1 and themselves). Every number can be expressed as a product of its prime factors. For example, 12 = 2 × 2 × 3 = 2² × 3.
Prime factorization is expressing a number as a product of prime numbers. For example, 60 = 2² × 3 × 5. This is useful for finding GCF, LCM, and simplifying fractions.
To find factors: 1) Start from 1 and check each number up to the square root. 2) If a number divides evenly, both it and the quotient are factors. For 36: 1×36, 2×18, 3×12, 4×9, 6×6 gives factors 1,2,3,4,6,9,12,18,36.
A perfect number equals the sum of its proper factors (factors excluding itself). The first few perfect numbers are 6 (1+2+3), 28 (1+2+4+7+14), and 496. Perfect numbers are rare and fascinating.
Last updated: 2025-01-15
Number of Factors
12
Composite number
60 is a composite number