Factor Calculator

Factors of 667

The factors of 667 are 1, 23, 29, and 667. In total, 667 has 4 factors. Its prime factorization is 23 × 29, and the sum of all its factors is 720.

All factors of 667

Here are all 4 factors of 667, listed from smallest to largest.

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Factor pairs of 667

These 2 pairs of whole numbers each multiply to give 667.

1 × 667 = 667
23 × 29 = 667

Prime factorization of 667

Dividing 667 by the smallest prime at each step gives its prime factorization:

667 ÷ 23 = 29
29 ÷ 29 = 1
Result: 667 = 23 × 29 = 23 × 29

The distinct prime factors of 667 are 23, 29. To factorize any other number, use the prime factorization calculator.

Factor tree of 667

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

Factor tree of 6676672329
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 667

Number of factors4
Sum of factors720
Sum of proper factors53
Prime factorization23 × 29
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 667 interesting

  • 667 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.
  • 667 is a deficient number: its proper factors sum to 53, which is 614 less than 667 itself.

How to find the factors of 667 yourself

Divide 667 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 √66725.83, because every factor above that pairs with one below it.

667 ÷ 1 = 667
667 ÷ 23 = 29

Reading both columns gives every factor: 1, 23, 29, 667. The factor calculator does this automatically for any number.

Frequently asked questions about 667

What are the factors of 667?

The factors of 667 are 1, 23, 29, and 667. That is 4 factors in total, counting both 1 and 667.

Is 667 a prime number?

No, 667 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 667 is also divisible by 23.

What is the prime factorization of 667?

The prime factorization of 667 is 23 × 29. Written out in full: 23 × 29 = 667. Its distinct prime factors are 23, 29.

What two numbers multiply to give 667?

There are 2 pairs of whole numbers that multiply to 667: 1 × 667, 23 × 29.

What is the sum of the factors of 667?

Adding all the factors of 667 together gives 720. Excluding 667 itself, the proper factors sum to 53.

Is 667 a perfect square?

No, 667 is not a perfect square. There is no whole number that multiplies by itself to give 667. The nearest perfect squares are 625 and 676.

What is the largest factor of 667 other than itself?

The largest factor of 667 apart from 667 itself is 29, since 667 ÷ 29 = 23.

How many factors does 667 have?

667 has 4 factors: 1, 23, 29, and 667. You can verify this from the prime factorization 23 × 29: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 667 down further with the prime factorization calculator, or compare 667 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.