Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429

To do:

Here we have to express each of the given numbers as a product of its prime factors.

Solution:  

We know that,

Every positive integer greater than 1 can be written as a product of prime numbers (or the integer is itself a prime number). So,

• Composite number  $=$  Product of prime numbers

(i) Prime factorization of 140 is:

$140\ =\ 2\ \times\ 2\ \times\ 5\ \times\ 7$

$\mathbf{140\ =\ 2^2\ \times\ 5^1\ \times\ 7^1}$

Hence, 140 can be expressed as  $2^2\ \times\ 5^1\ \times\ 7^1$. 

(ii) Prime factorization of 156 is:

$156\ =\ 2\ \times\ 2\ \times\ 3\ \times\ 13$

$\mathbf{156\ =\ 2^2\ \times\ 3^1\ \times\ 13^1}$

Hence, 156 can be expressed as  $2^2\ \times\ 3^1\ \times\ 13^1$. 

(iii) Prime factorization of 3825 is:

$3825\ =\ 3\ \times\ 3\ \times\ 5\ \times\ 5\ \times\ 17$

$\mathbf{3825\ =\ 3^2\ \times\ 5^2\ \times\ 17^1}$

Hence, 3825 can be expressed as  $3^2\ \times\ 5^2\ \times\ 17^1$. 

(iv) Prime factorization of 5005 is:

$5005\ =\ 5\ \times\ 7\ \times\ 11\ \times\ 13$

$\mathbf{5005\ =\ 5^1\ \times\ 7^1\ \times\ 11^1\ \times\ 13^1}$

Hence, 5005 can be expressed as  $5^1\ \times\ 7^1\ \times\ 11^1\ \times\ 13^1$. 

(v) Prime factorization of 7429 is:

$7429\ =\ 17\ \times\ 19\ \times\ 23$

$\mathbf{7429\ =\ 17^1\ \times\ 19^1\ \times\ 23^1}$

Hence, 7429 can be expressed as  $17^1\ \times\ 19^1\ \times\ 23^1$. 

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Updated on: 10-Oct-2022

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