Factors of 112 Using Prime Factorization
Factors of 112
What are the Factors of 112?
Numbers that divide 112 without leaving any remainder are known as factors of 112.
For Example: 4 is a factor of 112 because when we divide 112 by 4 it gives us the quotient as 28 and the remainder will be 0. Here the quotient is also a factor of 112.
So to check if the number is a factor of 112 or not, divide 112 by that number and verify whether the remainder is zero or not.
Factor List of 112
We can stop checking after 9 as the factor pairs start to repeat.
Therefore the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
Prime Factors of 112
The number 112 is known as a composite number, which implies that it has more than two factors. To find the prime factors, we first divide the number 112 by its smallest prime factor, that is, 2.
112 ÷ 2 = 56
Again, divide by 2, and continue doing so;
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
Now, divide by the next prime number, that is, 7.
7 ÷ 7 = 1
So, the prime factorization of 112 = 2 × 2 × 2 × 2 × 7 or 2\( ^4 \) × 7.
This means that 2 and 7 are the prime factors of 112.
Factor Pairs of 112
The factor pair of a number is a set of its two factors that when multiplied together result in the original number.
Example: (7, 16) is the factor pair of 112 as 7 x 16 = 112.
The factor pair can be a positive pair or a negative pair.
Positive Factor Pairs of 112
We can define factor pairs as a pair of factors of a number that when the multiplied result in the number. It is clear from the table that every pair of numbers when multiplied results in 112.
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Rapid Recall
Factors of 112 are;
Solved Factors of 112 Examples
Example 1: Find the common factors of 112 and 119.
Solution:
Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112
Factors of 119 = 1, 7, 17, and 119
Therefore, the common factors of 112 and 119 are 1 and 7.
Example 2: Find the common factors of 112 and 107.
Solution:
Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112
Factors of 107 = 1 and 107
Therefore, the common factor of 112 and 107 is 1.
Example 3: Find the greatest common factor of 72 and 112.
Solution:
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
Factors of 112 = 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112
The common factors of 72 and 112 are 1, 2, 4, and 8.
Therefore, the greatest common factor of 72 and 112 is 8.
Example 4: A store owner has 112 packs of cereal. He wants to arrange these packs in a rectangular array. How many different arrays can he make?
Solution:
To find the number of arrays that can be made we need the number of factor pairs of 112.
112 has 5 factor pairs.
Each pair can be arranged in 2 different ways to make rectangular arrays.
So the number of possible rectangular arrays = (2 x 5)
= 10
Therefore the store owner can arrange the packs in 10 different ways.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112
So, the least factor of 112 is 1 and the greatest factor is 112 itself.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112
Sum of factors = 1 + 2 + 4 + 7 + 8+ 14 + 16 + 28 + 56 + 112 = 248
So, the sum of factors of 112 is 248.
Yes, 14 is a factor of 112. Because when the number 112 is divided by 14, it results in 8 as the quotient, and 0 as the remainder.
When the number 112 is multiplied by any natural number, the result is known as a multiple of 112.
The factor of 112 is the number that divides 112 exactly, leaving zero as the remainder.
The negative factor pairs are a set of two negative numbers which when multiplied together give the original number.
So, the negative factor pairs of 112 are,
(- 1, – 112), (- 2, – 56), (- 4, – 28), (- 7, – 16) and (- 8, – 14).