# EXPRESSING NUMBERS AS A PRODUCT OF PRIME FACTORS WORKSHEET

When we are expressing the given number as product of primes factors, we have to be aware the divisibility rules for 2,3, 5.... etc.

Divisibility rule for 2 :

Every even number is divisible by 2. The number which ends with 0, 2 4, 6 or 8 are even numbers and it is divisible by 2.

Divisibility rule for 3 :

If the sum of the number is divisible by 3, then the given number is also divisible by 3.

Divisibility rule for 5 :

If the number ends with 0 or 5, then it is divisible by 5.

To express the given number as product of prime factors, we follow the steps:

Step 1 :

Divide the given number using prime numbers.

Step 2 :

Until we receive prime number, we have to continue the process.

Step 3 :

Write the factors as product.

Step 4 :

If we see the repeated factor, write the repeating factor in exponential form.

Express the following numbers as product of prime factors.

Problem 1 :

52

Solution :

In 52, the unit digit is 2. So, it is even number. Then it is divisible by 2.

52 = 2 x 2 x 13

Here 2 is repeating two times and no more factors which are repeating.

Writing in the exponential form, we get

52 = 22 x 13

Problem 2 :

90

Solution :

The given number 90 ends with 0. Then, it must be the multiple of 2.

90 = 2 x 5 x 3 x 3

3 is repeating two times and no more factors are repeating. Writing in the exponential form, we get

= 2 x 5 x 32

Problem 3 :

72

Solution :

The given number 72 ends with 2. Then, it must be the multiple of 2.

72 = 2 x 2 x 2 x 3 x 3

The factor 2 is repeating three times and the factor 3 is repeating two times. Then, writing the repeating factors in exponential form.

= 23 x 32

Problem 4 :

100

Solution :

Since 100 ends with 0, it must be multiple of 2 or 5.

100 = 2 x 2 x 5 x 5

The factor 2 is repeating two times and the factor 5 is repeating two times. Then, writing the repeating factors in exponential form.

100 = 22 x 52

Problem 5 :

64

Solution :

Since 64 ends with 4, it must be multiple of 2.

64 = 2 x 2 x 2 x 2 x 2 x 2

The factor 2 is repeating six times. Then, writing the repeating factors in exponential form.

64 = 26

Problem 6 :

105

Solution :

Since 105 ends with 5, it must be divisible by 5.

105 = 5 x 3 x 7

Since there is no repeating factor, so we cannot express it in exponential form.

Problem 7 :

120

Solution :

Since 120 ends with 0, it must be divisible by 2.

120 = 2 x 2 x 2 x 3 x 5

The factor 2 is repeating three times and no more factor is repeating. Then, writing the repeating factors in exponential form.

120 = 23 x 3 x 5

Problem 8 :

85

Solution :

Since 85 ends with 5, it must be divisible by 5.

85 = 5 x 17

Problem 9 :

96

Solution :

Since 96 ends with 6, it must be divisible by 2.

96 =  2 x 2 x 2 x 2 x 2 x 3

The factor 2 is repeating five times and no more factor is repeating. Then, writing the repeating factors in exponential form.

96 =  25 x 3

Problem 10 :

112

Solution :

Since 112 ends with 2, it must be divisible by 2.

112 =  2 x 2 x 2 x 2 x 7

The factor 2 is repeating four times  and no more factor is repeating. Then, writing the repeating factors in exponential form.

112 =  24 x 7

Problem 11 :

84

Solution :

Since 84 ends with 4, it must be divisible by 2.

84 =  2 x 2 x 3 x 7

Since 2 is repeating 2 times and no more factors are repeating. We can write it in exponential form.

84 =  22 x 3 x 7

Problem 12 :

108

Solution :

Since 108 ends with 8, it must be divisible by 2.

108 =  2 x 2 x 3 x 3 x 3

Since 2 is repeating 2 times and 3 is repeating three times. So, we can write in the exponential form.

108 =  22 x 33

Problem 13 :

56

Solution :

Since 56 ends with 6, it must be divisible by 2.

56 =  2 x 2 x 2 x 7

Since 2 is repeating 3 times and no more factor is repeating. So, we can write in the exponential form.

56 =  23 x 7

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