Question

Choose the prime factorization of 112.
A) $2 \times 2 \times 2 \times 7$
B) $2 \times 2 \times 2 \times 2 \times 7$
C) $3 \times 3 \times 3 \times 7$
D) $3 \times 3 \times 3 \times 3 \times 7$

Answer 1

Hint: Here we have to use the concept of prime factorization to evaluate the factors of 112.
Any composite number , $x$ can be expressed in terms of its prime factors as ${a^m} \times {b^n}$ , where a,b,m and n are natural numbers, that is:
$x = {a^m} \times {b^n}$ .

Complete step by step answer:
So Factorizing 112 we will get:

That is, we can write $112$ as
$112 = 2 \times 2 \times 2 \times 2 \times 7 \times 1$
That is the factors of 112 are 2 which is being multiplied with itself 4 times and 7.

Hence the correct answer for the factors of 112 is option 2).

Note: Factorization means simplifying and expressing a number as powers of its prime factors. A prime number has only 1 and itself as the factors, while a composite number has numbers other than 1 or the number itself as the factors. All even numbers except 2 are composite numbers. For example 8, now 8 has factors other than 1 and 8 itself as 2. So 8 is a composite number hand. On the other hand 13, has no other factor except 1 and 13, and hence 13 is a prime number.