Factors are the pair of numbers which on multiplication gives us the original number. Factors are also defined as the number which on dividing the original number gives us the quotient as a whole number. Factors can be positive numbers or negative numbers. Decimal numbers and fractions cannot be the factor. Factors and multiples are not the same. Multiples are the extended terms of the given number. There are different methods by which we can find the factors. They are factorization method, prime factorization method, division method, divisibility method.
We will discuss all these methods in detail further.
40 ÷ 1 = 40 |
40 ÷ 2 = 20 |
40 ÷ 3 = not divisible |
40 ÷ 4 = 10 |
40 ÷ 5 =8 |
40 ÷ 6 = not divisible |
40 ÷ 7 = not divisible |
40 ÷ 8 = 5 |
40 ÷ 9 = not divisible |
40÷ 10 = 4 |
40 ÷ 11 = not divisible |
40 ÷ 12 = not divisible |
40 ÷ 13 = not divisible |
40 ÷ 14 = not divisible |
40 ÷ 15 = not divisible |
40 ÷ 16 = not divisible |
40 ÷ 17 = not divisible |
40 ÷ 18 = not divisible |
40 ÷ 19 = not divisible |
40 ÷ 20 = 2 |
Following the multiplication tables up to 20, we can easily find the factors of 40.
So, the factors of 40 are 40, 20, 10, 8, 5, 4, and 2.
In order to find more factors of 40, we can start dividing 40 with the factors that we have obtained until now.
40 ÷ 40= 1 |
40 ÷ 20 = 2 |
40 ÷ 10 = 4 |
40 ÷ 8 = 5 |
40 ÷ 5 = 8 |
40 ÷ 4 = 10 |
40 ÷ 2 = 20 |
The common factors for 40 are 2, 4, 5, 8, 10, 20.
In this method, we check the divisibility of 40 by every number. This is the simplest method to find the factors of 40.
We will check whether the number is divisible by 2 since 40 is the even number is divisible by 2.
Now we will check the divisibility by 3. 40 is not divisible by 3.
Now by 4, it is divisible because multiplying 4 by 10 gives us 40.
It is also divisible by 5 because it has 0 in the unit’s place.
Similarly, we will check the divisibility till 10 and we will get all the factors of 40.
1. What do you understand by the factorization method to find the factors?
In this method, we first find the multiple of 40 that is 1 and 40. Then we find more numbers which on multiplication gives 40. 2 and 20 is the next pair of factors.
We will discuss the steps to find the factors of 40 by factorization method.
First, we need to write the number that is 40.
Find the 2 numbers, which provides the result as 40 after the multiplication, so 2 × 20 = 40 therefore 2 and 20 are the factors of 40.
We know that 2 is the prime which has only two factors that are 1 and 2. So, it cannot be further factorized.
Now we will consider 20 which is a composite number and it can be factorized further,
20= 2× 2 × 5 × 1
Therefore, the factorization of 40 is expressed as 40= 2×2 ×2 × 5 × 1.
2. How to find the factors of 40 using the prime factorization method?
In this method, we find out all prime factors of the given number. There are some steps that we need to follow to find factors of 40.
First, we need to write the given number here the number is 40.
Now we will start dividing 40 by the smallest prime number that is 2.
We will get 40÷ 2 = 20.
Now, this can be again divided by 2 so we will divide it,
20 ÷ 2= 10.
Again we will divide it by 2.
10 ÷ 2 = 5
Now we cannot divide 5 by 2, so we will divide with the next prime the number is 3.
Dividing 5 by 3 gives us a decimal number which cannot be the factor.
So now we will divide it by next prime number 5 which gives us
5 ÷ 5 = 1
So the prime factorization of 40 is 2×2×2×5 which can also be written as 23 × 5 where 2 and 5 are prime numbers.
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