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Number 60 is a composite number and we will find how to find the factors of 60. We will also see techniques to find out the Prime factorisation of 60 easily
Factors of 60
A factor of a number is an exact divisor of that number. So factors of 60 are the numbers which are exact divisors of 60.
Factors of any number can be found by finding the number which divides the number without remainder, or alternatively, numbers that can multiply together to equal the target number being converted
Let us check how to find the factors
Method -1
Factors can be found by finding the numbers which when multiplied together give the number 60. Now to find the numbers we can start with the integer 1 and keep increasing it by 1 and we will discard where the other number cannot be found. We will stop at a point where we start seeing the repetition of numbers We will find the multiplication one by one and start writing it down. So
$60 = 1 \times 60$
$60 = 2 \times 30 $
$60 = 3 \times 20$
$60 = 4 \times 15 $
$60 = 5 \times 12$
$60 = 6 \times 10 $
$60 = 10 \times 6$
We can stop here as 10 and 6 have occurred earlier.
So factors are 1,60,2,30,3,20,4,15,5,12,6,10
Putting the factors in ascending order, we get
1,2,3,4,5,6,10,12,15,20,30,60
Method -2
Factors can be found by finding the numbers which divide the number without a remainder. We can start with the following sequence: 1,2,3,4… and go till the mid-point of that number.
No Remainder
$60/2 = 30$ . No Remainder
$60/3 = 20$. No remainder
$60/4=15$. No remainder.
$60/5=12 $. No remainder.
$60/6=10 $. No remainder.
$60/10=6 $. No remainder.
$60/12=5 $. No remainder.
$60/15=4 $. No remainder.
$60/20 = 4$. No remainder.
$60/30=2$. No remainder.
So factors are 1,2,3,4,5,6,10,12,15,20,30,60
Hence Factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60
prime factorization of 60
When a number is expressed as a product of its factors we say that the number has been factorized. When the factorization contains the prime number only then it is called prime factorization.
Now let us look at how to find the prime factorization
There are two methods that can be used.
Division method
We divide the number 60 by 2, 3,4,5,6,7, etc. in this order repeatedly so long as the quotient is divisible by that number.
Thus, the prime factorization is $2 \times 2 \times 3 \times 5$ or $2^2 \times 3 \times 5$
Factor Tree Method
In this method, we first think about any two factors, and then we think about two factors of respective numbers. This goes till the factors are prime.
We can have many factor trees depending on the starting point but all of them will show the same prime factors.
Let’s check the different Factor trees for number 60
Hence the Prime Factorization is $2^2 \times 3 \times 5$
Factor of 60 in pair
We can find the factors of number 60 in pairs, by multiplying two numbers in a pair to get the original number as 60, such as:
$60 = 1 \times 60$
$60 = 2 \times 30 $
$60 = 3 \times 20$
$60 = 4 \times 15 $
$60 = 5 \times 12$
$60 = 6 \times 10 $
$60 = 10 \times 6$
So factor in pair are (1,60) , (2,30) ,(3,20), (4,15) ,(5,12), (6,10)
Hope you like the post
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