What are all the factors, the prime factorization, and factor pairs of 1200?

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 1200 , you can use the division method.

   1. Begin by dividing 1200 by the smallest possible number, which is 2.

   2. If the division is even, then 2 is a factor of 1200.

   3. Continue dividing 1200 by larger numbers until you find an odd number that does not divide evenly into 1200 .

   4. The numbers that divide evenly into 1200 are the factors of 1200 .

Now let us find how to calculate all the factors of One thousand two hundred :

    1200 ÷ 1 = 1200
    1200 ÷ 2 = 600
    1200 ÷ 3 = 400
    1200 ÷ 4 = 300
    1200 ÷ 5 = 240
    1200 ÷ 6 = 200
    1200 ÷ 8 = 150
    1200 ÷ 10 = 120
    1200 ÷ 12 = 100
    1200 ÷ 15 = 80
    1200 ÷ 16 = 75
    1200 ÷ 20 = 60
    1200 ÷ 24 = 50
    1200 ÷ 25 = 48
    1200 ÷ 30 = 40
    1200 ÷ 40 = 30
    1200 ÷ 48 = 25
    1200 ÷ 50 = 24
    1200 ÷ 60 = 20
    1200 ÷ 75 = 16
    1200 ÷ 80 = 15
    1200 ÷ 100 = 12
    1200 ÷ 120 = 10
    1200 ÷ 150 = 8
    1200 ÷ 200 = 6
    1200 ÷ 240 = 5
    1200 ÷ 300 = 4
    1200 ÷ 400 = 3
    1200 ÷ 600 = 2
    1200 ÷ 1200 = 1

As you can see, the factors of 1200 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 20 , 24 , 25 , 30 , 40 , 48 , 50 , 60 , 75 , 80 , 100 , 120 , 150 , 200 , 240 , 300 , 400 , 600 and 1200 .

The factors of 1200 are the numbers that can evenly divide 1200 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 20 , 24 , 25 , 30 , 40 , 48 , 50 , 60 , 75 , 80 , 100 , 120 , 150 , 200 , 240 , 300 , 400 , 600 and 1200.

Thus, there are a total of 30 factors of 1200

Factor Pairs of 1200 are combinations of two factors that when multiplied together equal 1200. There are many ways to calculate the factor pairs of 1200 .

One easy way is to list out the factors of 1200 :
   1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 20 , 24 , 25 , 30 , 40 , 48 , 50 , 60 , 75 , 80 , 100 , 120 , 150 , 200 , 240 , 300 , 400 , 600 , 1200

Then, pair up the factors:
   (1,1200),(2,600),(3,400),(4,300),(5,240),(6,200),(8,150),(10,120),(12,100),(15,80),(16,75),(20,60),(24,50),(25,48) and (30,40) These are the factor pairs of 1200 .

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 1200 using a factor tree, we would start by writing 1200 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 1200 would be 2 x 2 x 2 x 2 x 3 x 5 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 1200 using this method, we keep dividing until it gives a non-zero remainder.

    1200 ÷ 2 = 600
    600 ÷ 2 = 300
    300 ÷ 2 = 150
    150 ÷ 2 = 75
    75 ÷ 3 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So the prime factors of 1200 are 2 x 2 x 2 x 2 x 3 x 5 x 5.

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