Factors the 56 space all together numbers that fully divide the number 56 and when multiplied in pairs give the product as 56. These components of 56 are hopeful numbers yet can be an adverse as well. The number 56 is an even composite number, which way that it has actually several factors. In this lesson, we will certainly calculate the factors of 56, prime determinants of 56, and determinants of 56 in pairs in addition to solved instances for a far better understanding.
You are watching: What is the prime factorization of 56
|1.||What room the components of 56?|
|2.||How come Calculate components of 56?|
|3.||Factors the 56 by prime Factorization|
|4.||Factors the 56 in Pairs|
|5.||FAQs on determinants of 56|
What room the components of 56?
The determinants of 56 are integers that division 56 without any type of remainder. For example, 8 is a element of 56 because 8 divides 56 without any remainder. Interestingly, 7, i m sorry is the quotient that the above division, is also a element of 56.Check whether you acquire 0 together the remainder by splitting 56 by 8 using lengthy division.
To understand the concept of finding factors by prime factorization better, let united state take a few more examples.
The steps to uncover the factors of any kind of number:Divide the number by 2 and get another number. If the result number is no an integer, then round it come the nearest integer. Divide the given number by every of the numbers from 1 to the resultant number (from step 1) and see i beg your pardon of them outcomes in the remainder 0. We divide just by these numbers as any type of number the is better than half of a provided number cannot be that is factor. The divisor of each such department (with remainder 0) is the components of the number. Also, the provided number is additionally a element of itself.
Finding the determinants of 56
Divide 56 by 2, we gain 28. Divide 56 by each of the numbers from 1 come 28 and view which of them would offer the remainder 0. The divisors of every such divisions are the factors. Also, 56 is a factor of itself. Thus, 1,2,4,7,8,14,28 and also 56 room the components of 56.
Fractions and decimals that space not integers cannot be the factors of any type of numberWhen a number is a variable of the given number, climate its additive inverse is likewise a variable of the offered number.For example, because 8 is a variable of 56, -8 is additionally a aspect of 56.
Let us uncover the prime factorization the 56 by to express it as the product of prime numbers.
So the prime factorization the 56 is 2 × 2 × 2 × 7.From the prime factorization of 56, the is clear that 2 and also 7 space the factors of 56. In fact, 2 and also 7 space the prime components of 56. Also, we recognize that 1 is a variable of every number. Thus, The determinants of 56 by prime factorization are 1, 2, 4, 7, 8, 14, 28, and also 56.
While detect the determinants of a number keep the following in mind:1 and the number chin are always the components of a number.To find the other components of the number, we an initial find its element factorization. Then, the multiplicands that the prime factorization room the prime factors of the number.By multiplying part or all multiplicands in various combinations, we acquire the composite determinants of the number.
The pair factors of 56 are derived by composing 56 together a product of 2 numbers in all feasible ways.
In each product, both multiplicands are the components of 56.
1 x 56
2 x 28
4 x 14
7 x 8
The negative pair components of 56 room (-1, -56), (-2, -28), (-4, -14), and also (-7, -8).
Example 1 Evelyn is a course teacher and also her class has 56 students. She desires to divide her class into groups and give lock groupwise mathematics practice. In how numerous ways can she team 56 students therefore that:
A group cannot have 1 or every students of the class.
Each group has an equal number of students.
We currently learned the the determinants of 56 room 1, 2, 4, 7, 8, 14, 28, and 56. But the groups cannot have actually one or every students. Therefore we overlook 1 and 56. The other components 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 discover the element factorization that 56 in his exam, he did it in the following method and answered that the element factorization of 56 is 2 × 7. However, his teacher marked it wrong. Can we assist Jamie by mirroring him the correct way to calculate prime factorization?
Prime factorization provided by Jamie is = 2 × 7It is not correct. Permit us shot factor tree method to find prime administer of 56.
Thus, the prime factorization that 56 is 23 × 7.
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