Factors of 56 are all such numbers that completely divide the number 56 and when multiplied in pairs give the product as 56. These factors of 56 are positive numbers but can be negative as well. The number 56 is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 56, prime factors of 56, and factors of 56 in pairs along with solved examples for a better understanding.
You are watching: Write 56 as a product of prime factors
|1.||What Are the Factors of 56?|
|2.||How to Calculate Factors of 56?|
|3.||Factors of 56 by Prime Factorization|
|4.||Factors of 56 in Pairs|
|5.||FAQs on Factors of 56|
What Are the Factors of 56?
The factors of 56 are integers that divide 56 without any remainder. For example, 8 is a factor of 56 because 8 divides 56 without any remainder. Interestingly, 7, which is the quotient of the above division, is also a factor of 56.Check whether you get 0 as the remainder by dividing 56 by 8 using long division.
To understand the concept of finding factors by prime factorization better, let us take a few more examples.
The steps to find the factors of any number:Divide the number by 2 and get another number. If the resultant number is not an integer, then round it to the nearest integer. Divide the given number by each of the numbers from 1 to the resultant number (from step 1) and see which of them results in the remainder 0. We divide only by these numbers as any number that is greater than half of a given number cannot be its factor. The divisor of each such division (with remainder 0) is the factors of that number. Also, the given number is also a factor of itself.
Finding the Factors of 56
Divide 56 by 2, we get 28. Divide 56 by each of the numbers from 1 to 28 and see which of them would give the remainder 0. The divisors of all such divisions are the factors. Also, 56 is a factor of itself. Thus, 1,2,4,7,8,14,28 and 56 are the factors of 56.
Fractions and decimals that are not integers cannot be the factors of any numberWhen a number is a factor of the given number, then its additive inverse is also a factor of the given number.For example, since 8 is a factor of 56, -8 is also a factor of 56.
Let us find the prime factorization of 56 by expressing it as the product of prime numbers.
So the prime factorization of 56 is 2 × 2 × 2 × 7.From the prime factorization of 56, it is clear that 2 and 7 are the factors of 56. In fact, 2 and 7 are the prime factors of 56. Also, we know that 1 is a factor of every number. Thus, The factors of 56 by prime factorization are 1, 2, 4, 7, 8, 14, 28, and 56.
While finding the factors of a number keep the following in mind:1 and the number itself are always the factors of a number.To find the other factors of the number, we first find its prime factorization. Then, the multiplicands of the prime factorization are the prime factors of the number.By multiplying some or all multiplicands in different combinations, we get the composite factors of the number.
The pair factors of 56 are obtained by writing 56 as a product of two numbers in all possible ways.
In each product, both multiplicands are the factors of 56.
1 x 56
2 x 28
4 x 14
7 x 8
The negative pair factors of 56 are (-1, -56), (-2, -28), (-4, -14), and (-7, -8).
Example 1 Evelyn is a class teacher and her class has 56 students. She wants to divide her class into groups and give them groupwise math practice. In how many ways can she group 56 students so that:
A group cannot have 1 or all students of the class.
Each group has an equal number of students.
We already learned that the factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. But the groups cannot have one or all students. So we ignore 1 and 56. The other factors of 56 are 2, 4, 7, 8, 14, and 28 (which are 6 in number).Thus,the required number of ways = 6
Example 2 When Jamie is asked to find the prime factorization of 56 in his exam, he did it in the following way and answered that the prime factorization of 56 is 2 × 7. However, his teacher marked it wrong. Can we help Jamie by showing him the correct way to calculate prime factorization?
Prime factorization given by Jamie is = 2 × 7It is not correct. Let us try factor tree method to find prime factorization of 56.
Thus, the prime factorization of 56 is 23 × 7.
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