Math Worksheets

Archive for the ‘Prime Factors’ Category

Dividing 17 by the NEXT smallest prime number, 3.

• 17 ÷ 3 = 5.6 recurring, not an integer (whole number so move on to the next prime number)

Dividing 17 by the next smallest prime number, 5.

• 17 ÷ 5 = 3.4, not an integer (whole number so move on to the next prime number)

Dividing 17 by the next smallest prime number, 7.

• 17 ÷ 7 = 2.43, not an integer (whole number so move on to the next prime number)

Dividing 17 by the nextsmallest prime number, 11.

• 17 ÷ 11 = 1.55, not an integer (whole number so move on to the next prime number)

Dividing 17 by the next smallest prime number, 13.

• 17 ÷ 31 = 1.31, not an integer (whole number so move on to the next prime number)

Dividing 17 by the next smallest prime number, 17.

• 17 ÷ 17 = 1 and the search for Prime factors concludes.

So, the Prime factors of 136 are 2 and 17. And, 136 can be written as a factor of:

136 = 2 x 2 x 2 x 17

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What are the Prime factors of 136?

Dividing 136 by the smallest prime number, 2.

136 ÷ 2 = 68

136 = 2 x 68

Dividing 68 by the smallest prime number, 2.

68 ÷ 2 = 34

136 = 2 x 2 x 34

Dividing 34 by the smallest prime number, 2.

34 ÷ 2 = 17

136 = 2 x 2 x 2 x 17

Dividing 17 by the smallest prime number, 2.

17 ÷ 2 = 8.5, not an integer (whole number so move on to the next prime number)

Once you have found a prime factor, keep dividing the remainder by the same prime factor until the remainder is no longer a whole number (an integer). When that happens, move on to the next prime number.

Prime factors are factors of another number that are Prime numbers.

What is a prime factor?

Prime factors are Prime numbers that are factors of an integer.

Finding prime factor

Finding prime factor is easy. Take a number and divide it by the smallest Prime numbers you know. An example of how to find prime factors is shown below.

What are prime factors of 25?

Step 1: Divide 25 by the smallest prime number you know. The smallest prime number you know is 2.

So, divide 25 by 2.

25 ÷ 2 = 12.5, not an integer (whole number), therefore the prime number 2 is not a prime factor of 25.

Step 2: Divide 25 by the NEXT smallest prime number you know. The NEXT smallest prime number you know is 3.

So, divide 25 by 3.

25 ÷ 3 = 8.3 recurring, not an integer (whole number), therefore the prime number 3 is not a prime factor of 25.

Step 3: Divide 25 by the NEXT smallest prime number you know. The NEXT smallest prime number you know is 5.

So, divide 25 by 5.

25 ÷ 5 = 5, an integer (whole number), therefore the prime number 5 is a prime factor of 25.

Step 4: Divide the remaining number by the same prime number (5 in this case) or the next smallest prime number you know (7).

Since the remaining number is 5, so divide 5 by 5.

5 ÷ 5 = 1.

Stop the process when the remainder of the divisions is 1.

That means, 25 has only one prime factor, 5.

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