Factors of 105

All factors of 105

Here are all 8 factors of 105, listed from smallest to largest.

Factor pairs of 105

These 4 pairs of whole numbers each multiply to give 105.

Prime factorization of 105

Dividing 105 by the smallest prime at each step gives its prime factorization:

The distinct prime factors of 105 are 3, 5, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 105

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Properties of 105

What makes 105 interesting

• 105 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
• 105 is a deficient number: its proper factors sum to 87, which is 18 less than 105 itself.
• 105 is a triangular number — it is the sum of the first 14 whole numbers (1 + 2 + … + 14 = 105).
• 105 has 3 distinct prime factors (3, 5, 7), which is why it has so many divisors.

How to find the factors of 105 yourself

Divide 105 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √105 ≈ 10.25, because every factor above that pairs with one below it.

Reading both columns gives every factor: 1, 3, 5, 7, 15, 21, 35, 105. The factor calculator does this automatically for any number.