What are all the factors, the prime factorization, and factor pairs of 735?

To find the factors of 735, divide 735 by each number starting with 1 and working up to 735

What is a factor in math ?

Factors are the numbers you multiply together to get another number. For example, the factors of 15 are 3 and 5 because 3 × 5 = 15.

The factors of a number can be positive or negative, but they cannot be zero.

The factors of a number can be used to find out if the number is prime or not.

A prime number is a number that has only two factors: itself and 1. For example, the number 7 is prime because its only factors are 7 and 1.

List all of the factors of 735 ?

To calculate the factors of 735 , you can use the division method.

   1. Begin by dividing 735 by the smallest possible number, which is 2.

   2. If the division is even, then 2 is a factor of 735.

   3. Continue dividing 735 by larger numbers until you find an odd number that does not divide evenly into 735 .

   4. The numbers that divide evenly into 735 are the factors of 735 .

Now let us find how to calculate all the factors of Seven hundred thirty-five :

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

As you can see, the factors of 735 are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 49 , 105 , 147 , 245 and 735 .

How to Write Numbers in French Similar to 735?

How many factors of 735 are there ?

The factors of 735 are the numbers that can evenly divide 735 . These numbers are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 49 , 105 , 147 , 245 and 735.

Thus, there are a total of 12 factors of 735

What are the factor pairs of 735 ?

Factor Pairs of 735 are combinations of two factors that when multiplied together equal 735. There are many ways to calculate the factor pairs of 735 .

One easy way is to list out the factors of 735 :
   1 , 3 , 5 , 7 , 15 , 21 , 35 , 49 , 105 , 147 , 245 , 735

Then, pair up the factors:
   (1,735),(3,245),(5,147),(7,105),(15,49) and (21,35) These are the factor pairs of 735 .

Prime Factorisation of 735

There are a few different methods that can be used to calculate the prime factorization of a number. Two of the most common methods are listed below.

1) Use a factor tree :

   1. Take the number you want to find the prime factorization of and write it at the top of the page

   2. Find the smallest number that goes into the number you are finding the prime factorization of evenly and write it next to the number you are finding the prime factorization of

   3. Draw a line under the number you just wrote and the number you are finding the prime factorization of

   4. Repeat step 2 with the number you just wrote until that number can no longer be divided evenly

   5. The numbers written on the lines will be the prime factors of the number you started with

For example, to calculate the prime factorization of 735 using a factor tree, we would start by writing 735 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 735 would be 3 x 5 x 7 x 7.

2) Use a factorization method :

There are a few different factorization methods that can be used to calculate the prime factorization of a number.

One common method is to start by dividing the number by the smallest prime number that will divide evenly into it.

Then, continue dividing the number by successively larger prime numbers until the number has been fully factorised.

For example, to calculate the prime factorization of 735 using this method, we keep dividing until it gives a non-zero remainder.

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

So the prime factors of 735 are 3 x 5 x 7 x 7.

Frequently Asked Questions on Factors

What are all the factors of 735 ?

The factors of 735 are 1 , 3 , 5 , 7 , 15 , 21 , 35 , 49 , 105 , 147 , 245 and 735.

What is the prime factorization of 735 ?

The prime factorization of 735 is 3 x 5 x 7 x 7 or 31 x 51 x 72, where 3 , 5 , 7 are the prime numbers .

What are the prime factors of 735 ?

The prime factors of 735 are 3 , 5 , 7 .

Is 735 a prime number ?

A prime number is a number that has only two factors 1 and itself.
735 it is not a prime number because it has the factors 1 , 3 , 5 , 7 , 15 , 21 , 35 , 49 , 105 , 147 , 245 and 735.

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