Prime Factorization of 735

What is the Prime Factorization of 735?

Answer: Prime Factors of 735: 3, 5, 7, 7

or

3 × 5 × 72

Explanation of number 735 Prime Factorization

Prime Factorization of 735 it is expressing 735 as the product of prime factors. In other words it is finding which prime numbers should be multiplied together to make 735.

Since number 735 is a Composite number (not Prime) we can do its Prime Factorization.

To get a list of all Prime Factors of 735, we have to iteratively divide 735 by the smallest prime number possible until the result equals 1.

Here is the complete solution of finding Prime Factors of 735:

The smallest Prime Number which can divide 735 without a remainder is 3. So the first calculation step would look like:

735 ÷ 3 = 245

Now we repeat this action until the result equals 1:

245 ÷ 5 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

Now we have all the Prime Factors for number 735. It is: 3, 5, 7, 7

Or you may also write it in exponential form: 3 × 5 × 72

Prime Factor Tree of 735

We may also express the prime factorization of 735 as a Factor Tree:

Prime factors of 735 factorization tree of 735

Prime Factorization Table

NumberPrime Factors
24 × 32 × 5
7, 103
2 × 192
3, 241
72422 × 181
52 × 29
2 × 3 × 112
727
23 × 7 × 13
36
2, 5, 73
73117, 43
22 × 3 × 61
733
7342, 367
3 × 5 × 72
25 × 23
73711, 67
2 × 32 × 41
739
22 × 5 × 37
3, 13, 19
7422, 7, 53
743743
74423 × 3 × 31
5, 149
7462, 373
32 × 83
22 × 11 × 17
7, 107

About "Prime Factorization" Calculator

This calculator will perform a Prime Factorization of any given number and will show all its Prime Factors. For example, it can help you find out what is the Prime Factorization of 735? (The answer is: 3, 5, 7, 7). Pick the number for factorization (e.g. '735'). After that hit the 'Calculate' button.
Prime factors are the positive integers having only two factors - 1 and the number itself

FAQ

What is the Prime Factorization of 735?

Prime Factors of 735: 3, 5, 7, 7

How many prime factors does 735 have?

Number 735 has 4 Prime Factors

What is the Prime Factorization of 735 in exponential form?

The Prime Factorization of the number 735 in the exponential form is: 3 × 5 × 72