Overview
In Math, factorisation is the breaking up of a number into smaller numbers. The lower numbers when multiplied together give you the original number. The process of splitting a number into its factors and divisors is known as factorisation. So factors of 56 will be some prime numbers that when multiplied, give the result, as 56. This is known as prime factorisation of 56. Factors of a number are those that are evenly divisible into another number. It is of immense importance in elementary arithmetic. It can be used in many ways like determining the least common multiple or highest common factor. Typically, we factorize a number till we reach a point where it can no longer be divisible. This is generally known as prime factorization.
Definition
When two numbers are multiplied together, and the result is a given number, then the two numbers are called factors of that particular number. For example, 5 x 3 equals 15; hence the numbers 5 and 3 are the factors of 15. The numbers that are multiplied together are called factor pairs.
What are the Factors of 56 in Pairs?
Every number is divisible by itself and one. For example, 56 /1 = 56. Since multiplication is the other side of the division, we can say that 56 x 1 = 56, so factors of 56 are 1 and 56. 1 and 56 are also known as factor pairs. Similarly, there are other factors and factor pairs of the number 56, such as
7 x 8 = 56 or 56/7 = 8 and 56/8 = 7
2 x 28 = 56 or 56/2= 28
4 x 14 = 56 or 56/4=14 and 56/14 = 4.
Therefore, the factor pairs of number 56 are 1 & 56, 7 & 8, 2 & 28, and 4 & 14.
Distinct Factors
You can consider 1, 2, 4, 7, 8, 14, 28, and 56 to be distinct factors of 56. Factors and distinct factors are the same. Factors are positive and are evenly divisible.
However, factors can be negative also. For example, it is -56, then the factors of – 56 are
-1 x 56 or 1 x -56 = -56
-2 x 28 or 2 x -28 = -56
-7 x 8 or 7 x -8 = -56
-4 x -14 or 4 x -14 = -56
In simple words, negative factors are factors with a (-) negative sign. Similarly,
-1 x -56 = 56
-2 x -28 = 56
-7 x -8 = 56
-4 x -14 = 56
Calculation of the Factors
Only whole numbers and integers can be converted into factors. For 56 to be an integer, you should be able to write 56 without a fraction or decimal parts, e.g. 56/3, 23/56 or 56.01. For 56 to be an integer, it has to be the whole number that is not a fraction. Thus, 56 is an integer as well as a whole number. When you divide 56 by its factors, the remainder is always a zero. For example,
56/1 = 56, results in zero and is divided by 1
56/2 = 28, results in zero and is divided by 2
56/4 = 14, results in zero and is divided by 4
56/7 = 8, results in zero and is divided by 8.
56/56 = 1, results in zero and is divided by 1
56/ 28 = 2, results in zero and is divided by 28
56/8 = 7, results in zero and is divided by 8
56/14 = 4, results in zero and is divided by 14.
How to Write the Factors of 56
Let us start by writing the number 56 first. Now, we have enough knowledge about the factor and the factor pairs of 56, so let’s begin any pair. For example, 7 x 56
= 7 x 8 = 56
= 7 x 2 x 2 x 2 = 56
Now, 7 is a prime number and it cannot break down further like the number 8. 7 can be written only as 7 x 1. So, we write the factors of 56 as = 7 x 2 x2 x 2 x 1.
Let us take another factor pair, 2 and 28
= 2 x 28 = 56
= 2 x 14 x 2 = 56
= 2 x 7 x 2 x 2 = 56
= 2 x 2 x 2 x 7 = 56
= 2 x 2 x 2 x 7 = 56
= 2 x 2 x 2 x 7 x 1 = 56
Therefore, factors of 56 can be written as 7 x2 x 2 x 2 x 1. You will get the same answer with any other factor pair that you use. The conclusion is that the factors of number 56 are always written as 7 x2 x 2 x 2 x 1.
Prime Factorization of 56
Firstly, know that 56 is a composite number. You already know that 56 is a whole number as well as an integer (not a fraction and not a decimal). The multiplication can take 7 x 8 or 2 x 28, so 56 is a composite number. A composite number is made up of prime factors also. As you know, prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, and 31 as they have no other factors apart from 1.
To begin with, divide the number 56 with 2, one of its prime factors.
56/2 = 28
28/2 = 14
14/2 = 7
7/2 = 3.5, a fraction. So, the next option is
7/7 = 1
It puts a stop to further divisions. Hence, prime factors of 56 are written as 2 x 2 x 2 x 7 or 23 x 2 where 2 and 7 are the prime numbers. It is the prime factorization of 56.
Fun Facts about Factors
Factors are whole numbers, integers, and never decimals or fractions.
All the even numbers always have two as a factor.
All numbers that end with five have five as a factor.
All numbers ending with a zero have 2, 5 and 10 as factors.
Factors of 56
When two numbers are multiplied together, the result is 56, and the factors of 56 are the numbers that generate that result. The full numbers, positive or negative, but not a fraction or decimal number, are factor pairs of the number 56. Consider the factor pair of 56, which is written (1, 56) and (-1, -56). As a result, both positive and negative factor pairs of 11 can be considered. The factorization method will be used to identify the factors of an integer, 56. Using the prime factorization approach and several solved cases, we will discover the factors of 56, pair factors, and prime factors of 56 in this article.
1,2,4,7,8,14,28,56
What are the 56 Factors?
The factors of 56 are the numbers that divide 56 perfectly. In other terms, the factors of 56 are the integers multiplied in pairs to produce 56. The number 56 has several factors other than 1 and 56 since it is an even composite number. As a result, the 56 factors are 1, 2, 4, 7, 8, 14, 28, and 56.
1, 2, 4, 7, 8, 14, 28, and 56 are the factors of 56.
Prime Factorization of 56: 2×2×2×7 or 23 × 7.
Pair Factors of 56
Multiply the two numbers in a pair to produce the original number of 56; examples of such numbers are as follows:
As a result, the positive pair factors of 56 are (1, 56), (2, 28), (4, 14), and (5, 14), respectively (7, 8). (-1, -56), (-2, -28), (-4, -14), and (-1, -56) are the negative pair factors of 56, respectively (-7, -8).
56 Factors Using the Division Method
The factors of 56 can be calculated using the division method by dividing 56 by different consecutive integers. If the integers divide 56 perfectly, they are the 56 factors. Let's begin by dividing 56 by one, and then move on to the other integer values.
(Factor = 1 and remainder = 0) 56/1 = 56
(Factor = 2 and remainder = 0) 56/2 = 28
(Factor = 4 and remainder = 0) 56/4 = 14
(Factor = 7 and remainder = 0) 56/7 = 8
(Factor = 8 and remainder = 0) 56/8 = 7
(Factor = 14 and remainder = 0) 56/14 = 4
(Factor = 28 and remainder = 0) 56/28 = 2
(Factor = 56, remainder = 0) 56/56 = 1
As a result, the 56 factors are 1, 2, 4, 7, 8, 14, 28, and 56.
FAQs on Factors of 56
1. What are the Rules of Prime Factorization?
A prime number is divisible only by itself or by ‘1’. All non-prime numbers can be broken down into prime number factors (As we saw in the above case of factorisation for 56 where the factors came to 2 x 2 x 2 x 7 or 23 x 2. Let’s take another case of ‘12’. The steps for factorisation will be
12 = 6 x 2
12 = 4 x 3
12 = 2 x 2 x 3
The last step splits the factors such that only prime numbers are left (i.e. 2 and 3). After this point, it cannot be split any further.
2. What are the Facts About Prime Factorization?
A number that has 1 and the number itself as its factor, is called a prime number.
So, 2,3,5,7 etc are prime numbers. Once you reduce the higher numbers to all prime numbers it is called prime factorisation.
Take the case of 315
315 = 63 x 5
315 = 9 x 7 x 5
315 = 3 x 3 x 7 x 5
Prime factorization happens when we write a number as a product of all its prime factors. So prime factors of 315 are 3, 3, 7, and 5.
3. What is factorisation?
Factorisation in Mathematics is the breaking up of a number into smaller numbers. The lower numbers when multiplied together give you the original number. The process of splitting a number into its factors and divisors is known as factorisation. Hence factors of 56 will be some prime numbers that when multiplied, give the result, as 56. We factorize a number till we reach a point where it can no longer be divisible, it is generally known as prime factorization.
4. What is factorisation using division?
The factorisation is the process of reducing the bracket of a quadratic equation, instead of expanding the bracket and converting the equation to a product of factors that cannot be reduced further. For example, factorizing (x2+5x+6) to (x+2) (x+3). Here, (x+2) (x+3) is the factorisation of a polynomial (x2+5x+6). All these factors can be either variables, integers or algebraic expressions. A form of disintegration, factorisation entails the gradual breakdown of a polynomial into its factors.
5. Is the free pdf of Factors of 56 helpful?
Yes, the free PDF of factors of 56 is very helpful. This PDF can help you know about the factorisation of the number 56 and how the process is carried on. You will be able to know the factorisation using different methods and of the variables, integers or algebraic expression. It is very important to get your concepts clear as this concept will be complicated with every next class. The factorisation is an important concept in Mathematics and students should be thorough with the same. You can learn about factorisation with the help of Vedantu.