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.
Factor pairs of 735
These 6 pairs of whole numbers each multiply to give 735.
Prime factorization of 735
Dividing 735 by the smallest prime at each step gives its prime factorization:
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.
Properties of 735
| Number of factors | 12 |
|---|---|
| Sum of factors | 1368 |
| Sum of proper factors | 633 |
| Prime factorization | 3 × 5 × 7² |
| Prime or composite? | Composite |
| Even or odd? | Odd |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Deficient |
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 √735 ≈ 27.11, because every factor above that pairs with one below it.
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.
Related numbers
Numbers mathematically connected to 735.
Frequently asked questions about 735
What are the factors of 735?
Is 735 a prime number?
What is the prime factorization of 735?
What two numbers multiply to give 735?
What is the sum of the factors of 735?
Is 735 a perfect square?
What is the largest factor of 735 other than itself?
How many factors does 735 have?
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.