What are all the factors, the prime factorization, and factor pairs of 85200?

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 85200 , you can use the division method.

   1. Begin by dividing 85200 by the smallest possible number, which is 2.

   2. If the division is even, then 2 is a factor of 85200.

   3. Continue dividing 85200 by larger numbers until you find an odd number that does not divide evenly into 85200 .

   4. The numbers that divide evenly into 85200 are the factors of 85200 .

Now let us find how to calculate all the factors of Eighty-five thousand two hundred :

    85200 ÷ 1 = 85200
    85200 ÷ 2 = 42600
    85200 ÷ 3 = 28400
    85200 ÷ 4 = 21300
    85200 ÷ 5 = 17040
    85200 ÷ 6 = 14200
    85200 ÷ 8 = 10650
    85200 ÷ 10 = 8520
    85200 ÷ 12 = 7100
    85200 ÷ 15 = 5680
    85200 ÷ 16 = 5325
    85200 ÷ 20 = 4260
    85200 ÷ 24 = 3550
    85200 ÷ 25 = 3408
    85200 ÷ 30 = 2840
    85200 ÷ 40 = 2130
    85200 ÷ 48 = 1775
    85200 ÷ 50 = 1704
    85200 ÷ 60 = 1420
    85200 ÷ 71 = 1200
    85200 ÷ 75 = 1136
    85200 ÷ 80 = 1065
    85200 ÷ 100 = 852
    85200 ÷ 120 = 710
    85200 ÷ 142 = 600
    85200 ÷ 150 = 568
    85200 ÷ 200 = 426
    85200 ÷ 213 = 400
    85200 ÷ 240 = 355
    85200 ÷ 284 = 300
    85200 ÷ 300 = 284
    85200 ÷ 355 = 240
    85200 ÷ 400 = 213
    85200 ÷ 426 = 200
    85200 ÷ 568 = 150
    85200 ÷ 600 = 142
    85200 ÷ 710 = 120
    85200 ÷ 852 = 100
    85200 ÷ 1065 = 80
    85200 ÷ 1136 = 75
    85200 ÷ 1200 = 71
    85200 ÷ 1420 = 60
    85200 ÷ 1704 = 50
    85200 ÷ 1775 = 48
    85200 ÷ 2130 = 40
    85200 ÷ 2840 = 30
    85200 ÷ 3408 = 25
    85200 ÷ 3550 = 24
    85200 ÷ 4260 = 20
    85200 ÷ 5325 = 16
    85200 ÷ 5680 = 15
    85200 ÷ 7100 = 12
    85200 ÷ 8520 = 10
    85200 ÷ 10650 = 8
    85200 ÷ 14200 = 6
    85200 ÷ 17040 = 5
    85200 ÷ 21300 = 4
    85200 ÷ 28400 = 3
    85200 ÷ 42600 = 2
    85200 ÷ 85200 = 1

As you can see, the factors of 85200 are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 20 , 24 , 25 , 30 , 40 , 48 , 50 , 60 , 71 , 75 , 80 , 100 , 120 , 142 , 150 , 200 , 213 , 240 , 284 , 300 , 355 , 400 , 426 , 568 , 600 , 710 , 852 , 1065 , 1136 , 1200 , 1420 , 1704 , 1775 , 2130 , 2840 , 3408 , 3550 , 4260 , 5325 , 5680 , 7100 , 8520 , 10650 , 14200 , 17040 , 21300 , 28400 , 42600 and 85200 .

The factors of 85200 are the numbers that can evenly divide 85200 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 20 , 24 , 25 , 30 , 40 , 48 , 50 , 60 , 71 , 75 , 80 , 100 , 120 , 142 , 150 , 200 , 213 , 240 , 284 , 300 , 355 , 400 , 426 , 568 , 600 , 710 , 852 , 1065 , 1136 , 1200 , 1420 , 1704 , 1775 , 2130 , 2840 , 3408 , 3550 , 4260 , 5325 , 5680 , 7100 , 8520 , 10650 , 14200 , 17040 , 21300 , 28400 , 42600 and 85200.

Thus, there are a total of 60 factors of 85200

Factor Pairs of 85200 are combinations of two factors that when multiplied together equal 85200. There are many ways to calculate the factor pairs of 85200 .

One easy way is to list out the factors of 85200 :
   1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 , 12 , 15 , 16 , 20 , 24 , 25 , 30 , 40 , 48 , 50 , 60 , 71 , 75 , 80 , 100 , 120 , 142 , 150 , 200 , 213 , 240 , 284 , 300 , 355 , 400 , 426 , 568 , 600 , 710 , 852 , 1065 , 1136 , 1200 , 1420 , 1704 , 1775 , 2130 , 2840 , 3408 , 3550 , 4260 , 5325 , 5680 , 7100 , 8520 , 10650 , 14200 , 17040 , 21300 , 28400 , 42600 , 85200

Then, pair up the factors:
   (1,85200),(2,42600),(3,28400),(4,21300),(5,17040),(6,14200),(8,10650),(10,8520),(12,7100),(15,5680),(16,5325),(20,4260),(24,3550),(25,3408),(30,2840),(40,2130),(48,1775),(50,1704),(60,1420),(71,1200),(75,1136),(80,1065),(100,852),(120,710),(142,600),(150,568),(200,426),(213,400),(240,355) and (284,300) These are the factor pairs of 85200 .

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 85200 using a factor tree, we would start by writing 85200 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 85200 would be 2 x 2 x 2 x 2 x 3 x 5 x 5 x 71.

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 85200 using this method, we keep dividing until it gives a non-zero remainder.

    85200 ÷ 2 = 42600
    42600 ÷ 2 = 21300
    21300 ÷ 2 = 10650
    10650 ÷ 2 = 5325
    5325 ÷ 3 = 1775
    1775 ÷ 5 = 355
    355 ÷ 5 = 71
    71 ÷ 71 = 1

So the prime factors of 85200 are 2 x 2 x 2 x 2 x 3 x 5 x 5 x 71.

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