Question

How do you find all the factors of $ 44 $ ?

Answer 1

Hint: In this question, we need to find the factors of $ 44 $ . Here, we will determine the factors of $ 44 $ , using the method of prime factorization. One must be sure of all the factors so that no factor of the given number is left out from the list.

Complete step-by-step answer:
Here, we need to find the factors of $ 44 $ using prime factorization.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. In other words, it is a number that has at least one divisor other than $ 1 $ and the number itself.
A prime number is a natural number greater than $ 1 $ that is not a product of two smaller natural numbers.
In prime factorization, we start dividing the number by the first prime number $ 2 $ and continue to divide by $ 2 $ until we get a decimal or remainder. Then divide by $ 3,5,7,.... $ etc. until we get the remainder $ 1 $ with the factors as prime numbers. Then write the numbers as a product of prime numbers.
So, we know that $ 44 $ is a composite number.
Prime factorization is a method of finding prime numbers which multiply to make the original number.
Thus, prime factorization of $ 44 $ is,
 $ 44 = 2 \times 2 \times 11 $
Therefore, the possible combinations of factors of $ 44 $ are: $ 44 \times 1 $ , $ 22 \times 2 $ , $ 11 \times 4 $ .
So, all factors of $ 44 $ are: $ 1 $ , $ 2 $ , $ 4 $ , $ 11 $ , $ 22 $ and $ 44 $ .

Note: Every other number can be broken down into prime number factors, but the prime numbers are the basic building blocks of all the numbers. We should remember the method of finding factors so as to use it in other complex questions as well.