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Factors of 112

112 is an even composite number composed of products of primes. It has 10 factors. Let’s learn about factors of 112, prime factors of 112, factor tree for 112, factors of 112 in pairs, and the prime factorization of 112.

Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112
Prime Factorization of 112: 2 × 2 × 2 × 2 × 7

1.	What Are the Factors of 112?
2.	How to Calculate the Factors of 112?
3.	Factors of 112 by Prime Factorization
4.	Factors of 112 in Pairs
5.	FAQs on Factors of 112

What Are the Factors of 112?

Factors of a number are the exact divisors of the number leaving the remainder as 0. For exanple, let's divide 112 by 16.

16 is a factor of 112

1, 2, 4, 7, 8, 14, 16, 28, 56, and 112 are all the factors of 112.

How to Calculate the Factors of 112?

Find all the divisors of 112 by using the divisibility rules. 112 is divisible by 1 and itself. 112 is even, so divisibile by 2. Its last 2 digits are multiple of 4, so divisible by 4. By checking the divisibility with all the numbers, we determine all the factors of 112.

112 ÷ 2 = 56
112 ÷ 4 = 28
112 ÷ 7 = 16
112 ÷ 8 = 14

All the divisors and the quotient obtained on division form the factors of 112. Thus, the factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

Explore factors using illustrations and interactive examples.

Factors of 49: The factors of 49 are 1, 7, and 49.
Factors of 110: The factors of 110 are 1 , 2, 5, 10,11, 22, 55, and 110.
Factors of 28: The factors of 28 are 1, 2, 4, 7, 14, and 28.
Factors of 121: The factors of 121 are 1, 11, and 121.
Factors of 56: The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

Factors of 112 by Prime Factorization

Prime factorization is a way of expressing a number as a product of its prime factors.

Follow the steps given below to find the factors of 112 using prime factorization.

Find the smallest prime that exactly divides 112, and get the quotient.
Write the quotient thus obtained and find the smallest prime, divide it and obtain the quotient.
Again find the smallest prime that exactly divides the quotient obtained in step 2 and write the quotient.
Repeat the process until you obtain the quotient as 1.

\ Prime factorization of 112

Now that we have done the prime factorization of our number, we can multiply the factors obtained and get other factors.

Factors of 112 in Pairs

Factor pairs of 112 are the pairs of factors which, when multiplied together, result in a product equal to the number 112.
(1 × 112), (2 × 56), (4 × 28), (7 × 16), (8 ×14) make 112.
Thus, we have (1, 112), (-1, -112), (2, 56), (-2, -56), (4, 28), (-4, -28), (7, 16), (-7, -16), (8, 14), and (-8, -14) as the factors of 112 in ordered pairs.

Factors of 112 in pairs

Important Notes:

Factors of 112 are the numbers that exactly divide 112, without any remainder.
The prime factorization 112 is 112 = 2 × 2 × 2 × 2 × 7.
The number 112 has five pairs of distinct factors.

Example 1: Aaron bought a new house. He wants his house number in such a way that the number is the greatest common factor of 96 and 112. What number can he use as his house number?

Solution:

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

The factors of 112 are: 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

The greatest common factor of 96 and 112 is 16.

So the number that he can choose is 16.
Example 2: How do you draw a factor tree of 112?

Solution:

On dividing 112 by 56, we get 112 ÷ 56 = 2.

Go further and keep dividing. 56 ÷2 = 28, 28 ÷ 2 = 14, 14 ÷ 2 =7

Thus the prime factorization of 112 = 2 x 2 x 2 x 2 x 7 is obtained by drawing the factor tree of 112.
Example 3: Jolly has a set of number cards. She is given a task to segregate them as factors of 49 and factors of 112. How will she be able to do it?

7 16 4 7 49

Solution:

The factors of 49 are 1, 7, and 49.

The factors of 112 are 1, 2, 4, 7, 8 ,14, 16, 28, 56, and 112.

Factors of 49 Factors of 112

7 and 49 4, 7, 16