What are all the factors, the prime factorization, and factor pairs of 360?

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.

To calculate the factors of 360 , you can use the division method.

   1. Begin by dividing 360 by the smallest possible number, which is 2.

   2. If the division is even, then 2 is a factor of 360.

   3. Continue dividing 360 by larger numbers until you find an odd number that does not divide evenly into 360 .

   4. The numbers that divide evenly into 360 are the factors of 360 .

Now let us find how to calculate all the factors of Three hundred sixty :

    360 ÷ 1 = 360
    360 ÷ 2 = 180
    360 ÷ 3 = 120
    360 ÷ 4 = 90
    360 ÷ 5 = 72
    360 ÷ 6 = 60
    360 ÷ 8 = 45
    360 ÷ 9 = 40
    360 ÷ 10 = 36
    360 ÷ 12 = 30
    360 ÷ 15 = 24
    360 ÷ 18 = 20
    360 ÷ 20 = 18
    360 ÷ 24 = 15
    360 ÷ 30 = 12
    360 ÷ 36 = 10
    360 ÷ 40 = 9
    360 ÷ 45 = 8
    360 ÷ 60 = 6
    360 ÷ 72 = 5
    360 ÷ 90 = 4
    360 ÷ 120 = 3
    360 ÷ 180 = 2
    360 ÷ 360 = 1

As you can see, the factors of 360 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 30 , 36 , 40 , 45 , 60 , 72 , 90 , 120 , 180 and 360 .

The factors of 360 are the numbers that can evenly divide 360 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 30 , 36 , 40 , 45 , 60 , 72 , 90 , 120 , 180 and 360.

Thus, there are a total of 24 factors of 360

Factor Pairs of 360 are combinations of two factors that when multiplied together equal 360. There are many ways to calculate the factor pairs of 360 .

One easy way is to list out the factors of 360 :
   1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 30 , 36 , 40 , 45 , 60 , 72 , 90 , 120 , 180 , 360

Then, pair up the factors:
   (1,360),(2,180),(3,120),(4,90),(5,72),(6,60),(8,45),(9,40),(10,36),(12,30),(15,24) and (18,20) These are the factor pairs of 360 .

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 360 using a factor tree, we would start by writing 360 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 360 would be 2 x 2 x 2 x 3 x 3 x 5.

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 360 using this method, we keep dividing until it gives a non-zero remainder.

    360 ÷ 2 = 180
    180 ÷ 2 = 90
    90 ÷ 2 = 45
    45 ÷ 3 = 15
    15 ÷ 3 = 5
    5 ÷ 5 = 1

So the prime factors of 360 are 2 x 2 x 2 x 3 x 3 x 5.

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