Prime Factors of 735

Looking to get a list of the prime factors of 735? In this article we'll give you all of the information you need, including the definition of the prime factors of 735, how to calculate the prime factors of 735 (also known as the prime factorization of 735). As a bonus, we'll also list out the prime factor tree of 735 the product of prime factors of 735, and tell you how many prime factors 735 has.

Prime Factors of 735 Definition

Every number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 735, we're talking about the building blocks of the number. A prime factor is a positive integer that can only be divided by 1 and itself. The prime factors of 735 are all of the prime numbers in it that when multipled together will equal 735.

Let's look at how to find all of the prime factors of 735 and list them out.

How to Find the Prime Factors of 735

You'll often see the process of finding prime factors of 735 referred to as prime factorization. To get the prime factors of 735 we need to divide 735 by the smallest prime number possible. You then repeat the same process by taking the result and dividing that number by the smallest prime number. Eventually, you end up with the number 1.

This process creates something called a prime factor tree of 735. The prime numbers used in this tree are the prime factors of 735. Let's look at the prime factor tree for 735:

• 735 ÷ 3 = 245
• 245 ÷ 5 = 49
• 49 ÷ 7 = 7
• 7 ÷ 7 = 1

Put simply, all of the prime numbers that you used to divide above are the prime factors of 735 as well. So what we are left with is the answer to your search, the prime factors of 735:

3, 5, 7, and 7

How Many Prime Factors of 735 Are There?

If we count up all of the prime factors of 735 used in the prime factor tree above, we can see that 735 has a total of 4 prime factors.

Product of Prime Factors of 735

The prime factors shown above (3, 5, 7, and 7) are completely unique to 735. When we multiply all of them together the result will be 735 and this is what we call the product of prime factors of 735. The prime factor products of 735 are listed below:

3 x 5 x 7 x 7 = 735

So there you have it. A complete guide to the factors of 735. You should now have the knowledge and skills to go out and calculate your own factors and factor pairs for any number you like.

Feel free to try the calculator below to check another number or, if you're feeling fancy, grab a pencil and paper and try and do it by hand. Just make sure to pick small numbers!

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Prime Factors of 736