Prime Factorization of 735
What is the Prime Factorization of 735?
or
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:
Related Calculations
<a href="https://calculat.io/en/number/prime-factors-of/735">Prime factors of 735 - Calculatio</a>
Prime Factorization Table
| Number | Prime Factors |
|---|---|
| 720 | 24 × 32 × 5 |
| 721 | 7, 103 |
| 722 | 2 × 192 |
| 723 | 3, 241 |
| 724 | 22 × 181 |
| 725 | 52 × 29 |
| 726 | 2 × 3 × 112 |
| 727 | 727 |
| 728 | 23 × 7 × 13 |
| 729 | 36 |
| 730 | 2, 5, 73 |
| 731 | 17, 43 |
| 732 | 22 × 3 × 61 |
| 733 | 733 |
| 734 | 2, 367 |
| 735 | 3 × 5 × 72 |
| 736 | 25 × 23 |
| 737 | 11, 67 |
| 738 | 2 × 32 × 41 |
| 739 | 739 |
| 740 | 22 × 5 × 37 |
| 741 | 3, 13, 19 |
| 742 | 2, 7, 53 |
| 743 | 743 |
| 744 | 23 × 3 × 31 |
| 745 | 5, 149 |
| 746 | 2, 373 |
| 747 | 32 × 83 |
| 748 | 22 × 11 × 17 |
| 749 | 7, 107 |
About "Prime Factorization" Calculator
Prime factors are the positive integers having only two factors - 1 and the number itself