Exercise 1.1, 1

Exercise 1.1, 1

Express each number as a product of its prime factors:
(I) 140

Solution:

Let’s divide 140 by the smallest prime number, 2:

                = 140 ÷ 2 = 70

Let’s divide 70 by 2 again:

                = 70 ÷ 2 = 35

Let’s divide 35 by 5:

                = 35 ÷ 5 = 7

Since 7 is a prime number, we stop here.

Thus, the prime factorization of 140 is:

               = 140 = 2² × 5 × 7

Express each number as a product of its prime factors:
(II) 156

Solution:

Let’s divide 156 by 2:

               = 156 ÷ 2 = 78

Let’s divide 78 by 2 again:

               = 78 ÷ 2 = 39

Let’s divide 39 by 3:

              = 39 ÷ 3 = 13

Since 13 is a prime number, we stop here.

Thus, the prime factorization of 156 is:

              = 156 = 22 × 3 × 13

Express each number as a product of its prime factors:
(III) 3825

Solution:

Let’s divide 3825 by 3:

               = 3825 ÷ 3 = 1275

Let’s divide 1275 by 3 again:

               = 1275 ÷ 3 = 425

Let’s divide 425 by 5:

              = 425 ÷ 5 = 85

Let’s divide 85 by 5 again:

             = 85 ÷ 5 = 17

Since 17 is a prime number, we stop here.

Thus, the prime factorization of 3825 is:

            = 3825 = 32 × 52 × 17

Express each number as a product of its prime factors:
(IV) 5005

Solution:

Let’s divide 5005 by 5:

           = 5005 ÷ 5 = 1001

Let’s divide 1001 by 7:

          = 1001 ÷ 7 = 143

Let’s divide 143 by 11:

          = 143 ÷ 11 = 13

Since 13 is a prime number, we stop here.

Thus, the prime factorization of 5005 is:

        = 5005 = 5 × 7 × 11 × 13

Express each number as a product of its prime factors:
(V) 7429

Solution:

Let’s divide 7429 by 17:

          = 7429 ÷ 17 = 437

Let’s divide 437 by 19:

          = 437 ÷ 19 = 23

Since 23 is a prime number, we stop here.

Thus, the prime factorization of 7429 is:

          = 7429 = 17 × 19 × 23