Factors of 56 Using Prime Factorization
Factors of 56
What are the Factors of 56?
The integers that divide 56 without leaving any remainder are known as the factors of 56.
For example, 4 is a factor of 56 because when we divide 56 by 4, it leaves 14 as the quotient and 0 as the remainder. Here, the quotient is also a factor of 56.
So, to check if the number is a factor of 56 or not, divide 56 by that number and verify whether the remainder is zero or not.
Factor List of 56
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
The Prime Factors of 56
The number 56 is a composite number, that is, it has more than two numbers as factors. To find the prime factors, first we will divide the number 56 by its smallest prime factor, that is, 2.
56 ÷ 2 = 28
Again, divide it by 2:
28 ÷ 2 = 14
14 ÷ 2 = 7
Now, divide by it the next prime numbers, that is, 3, 5, 7, and so on.
7 ÷ 3 = 2 and it leaves 1 as the remainder, which is not a factor.
7 ÷ 5 = 1 and it leaves 2 as the remainder, which is not a factor.
So, divide by the next prime number, that is, 7.
7 ÷ 7 = 1
So, the prime factorization of 56 = 2 × 2 × 2 × 7 or 2\( ^3 \) × 7.
This means that 2 and 7 are the prime factors of 56.
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The Factor Pairs of 56
The factor pairs are two factors that, when multiplied together, give the original number as the result.
Example: (7, 8) is the factor pair of 56.
The factor pairs can be a positive pair or a negative pair.
The Positive Factor Pairs of 56
When two positive numbers are multiplied, the product is positive.
Hence, the positive factor pairs of 56 are (1, 56), (2, 28), (4, 14), and (7, 8).
Rapid Recall
Factors of 56 are :
Solved Factors of 56 Examples
Example 1: Find the common factor of 53 and 56.
Solution:
The factors of 53 = 1 and 53
The factors of 56 = 1, 2, 4, 7, 8, 14, 28, and 56.
Therefore, the common factor of 53 and 56 is 1.
Example 2: Find the common factors of 56 and 28.
Solution:
The factors of 56 = 1, 2, 4, 7, 8, 14, 28, and 56.
The factors of 28 = 1, 2, 4, 7, 14, and 28.
Therefore, the common factors of 56 and 28 are 1, 2, 4, 7, 14, and 28.
Example 3: Archer decides to divide 56 marbles among 7 of her friends. How can she divide the marbles equally?
Solution:
56 ÷ 7 = 8.
As 7 is a factor of 56, we get 0 as the remainder.
Therefore, to divide the marbles equally, Archer would have to give each of her 7 friends 8 marbles each.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
So, the smallest factor of 56 is 1 and the greatest factor is 56 itself.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
Sum of factors = 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120
So, the sum of the factors of 56 is 120.
Yes, 14 is a factor of 56 because when the number 14 divides 56, it leaves the remainder as 0.
The prime factorization of 56 is 2 × 2 × 2 × 7 or 2\( ^3 \) × 7.