Factor Calculator

Factors of 123

The factors of 123 are 1, 3, 41, and 123. In total, 123 has 4 factors. Its prime factorization is 3 × 41, and the sum of all its factors is 168.

All factors of 123

Here are all 4 factors of 123, listed from smallest to largest.

1341123

Factor pairs of 123

These 2 pairs of whole numbers each multiply to give 123.

1 × 123 = 123
3 × 41 = 123

Prime factorization of 123

Dividing 123 by the smallest prime at each step gives its prime factorization:

123 ÷ 3 = 41
41 ÷ 41 = 1
Result: 123 = 3 × 41 = 3 × 41

The distinct prime factors of 123 are 3, 41. To factorize any other number, use the prime factorization calculator.

Factor tree of 123

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

Factor tree of 123123341
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 123

Number of factors4
Sum of factors168
Sum of proper factors45
Prime factorization3 × 41
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 123 interesting

  • 123 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 123 is a deficient number: its proper factors sum to 45, which is 78 less than 123 itself.

How to find the factors of 123 yourself

Divide 123 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 √123 ≈ 11.09, because every factor above that pairs with one below it.

123 ÷ 1 = 123 ✓
123 ÷ 3 = 41 ✓

Reading both columns gives every factor: 1, 3, 41, 123. The factor calculator does this automatically for any number.

Numbers mathematically connected to 123.

Frequently asked questions about 123

What are the factors of 123?

The factors of 123 are 1, 3, 41, and 123. That is 4 factors in total, counting both 1 and 123.

Is 123 a prime number?

No, 123 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 123 is also divisible by 3.

What is the prime factorization of 123?

The prime factorization of 123 is 3 × 41. Written out in full: 3 × 41 = 123. Its distinct prime factors are 3, 41.

What two numbers multiply to give 123?

There are 2 pairs of whole numbers that multiply to 123: 1 × 123, 3 × 41.

What is the sum of the factors of 123?

Adding all the factors of 123 together gives 168. Excluding 123 itself, the proper factors sum to 45.

Is 123 a perfect square?

No, 123 is not a perfect square. There is no whole number that multiplies by itself to give 123. The nearest perfect squares are 121 and 144.

What is the largest factor of 123 other than itself?

The largest factor of 123 apart from 123 itself is 41, since 123 ÷ 41 = 3.

How many factors does 123 have?

123 has 4 factors: 1, 3, 41, and 123. You can verify this from the prime factorization 3 × 41: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 123 down further with the prime factorization calculator, or compare 123 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.