Factor Calculator

Factors of 735

The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735. In total, 735 has 12 factors. Its prime factorization is 3 × 5 × 7², and the sum of all its factors is 1368.

All factors of 735

Here are all 12 factors of 735, listed from smallest to largest.

135715213549105147245735

Factor pairs of 735

These 6 pairs of whole numbers each multiply to give 735.

1 × 735 = 735
3 × 245 = 735
5 × 147 = 735
7 × 105 = 735
15 × 49 = 735
21 × 35 = 735

Prime factorization of 735

Dividing 735 by the smallest prime at each step gives its prime factorization:

735 ÷ 3 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Result: 735 = 3 × 5 × 7 × 7 = 3 × 5 × 7²

The distinct prime factors of 735 are 3, 5, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 735

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

Factor tree of 735735324554977
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 735

Number of factors12
Sum of factors1368
Sum of proper factors633
Prime factorization3 × 5 × 7²
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 735 interesting

  • 735 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 735 is a deficient number: its proper factors sum to 633, which is 102 less than 735 itself.
  • 735 has 3 distinct prime factors (3, 5, 7), which is why it has so many divisors.

How to find the factors of 735 yourself

Divide 735 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 √73527.11, because every factor above that pairs with one below it.

735 ÷ 1 = 735
735 ÷ 3 = 245
735 ÷ 5 = 147
735 ÷ 7 = 105
735 ÷ 15 = 49
735 ÷ 21 = 35

Reading both columns gives every factor: 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. The factor calculator does this automatically for any number.

Frequently asked questions about 735

What are the factors of 735?

The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735. That is 12 factors in total, counting both 1 and 735.

Is 735 a prime number?

No, 735 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 735 is also divisible by 3.

What is the prime factorization of 735?

The prime factorization of 735 is 3 × 5 × 7². Written out in full: 3 × 5 × 7 × 7 = 735. Its distinct prime factors are 3, 5, 7.

What two numbers multiply to give 735?

There are 6 pairs of whole numbers that multiply to 735: 1 × 735, 3 × 245, 5 × 147, 7 × 105, 15 × 49, 21 × 35.

What is the sum of the factors of 735?

Adding all the factors of 735 together gives 1368. Excluding 735 itself, the proper factors sum to 633.

Is 735 a perfect square?

No, 735 is not a perfect square. There is no whole number that multiplies by itself to give 735. The nearest perfect squares are 729 and 784.

What is the largest factor of 735 other than itself?

The largest factor of 735 apart from 735 itself is 245, since 735 ÷ 245 = 3.

How many factors does 735 have?

735 has 12 factors: 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735. You can verify this from the prime factorization 3 × 5 × 7²: add 1 to each exponent and multiply, giving 2 × 2 × 3 = 12.

Explore more

Try another number in the factor calculator, break 735 down further with the prime factorization calculator, or compare 735 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.