Question

HCF of \[10\] and \[100\] is?

Answer 1

Hint: In order to find the HCF of \[10\] and \[100\] . We know that HCF means the Highest Common Factor. Factors are the numbers which we can multiply with each other to get new numbers. Common factors are those which can divide the numbers in integers i.e exactly. We can use the multiplication table and division rules to find the greatest common factors.

Complete step-by-step answer:
When all the factors of two or more numbers are found, and some of them are the same, the Greatest Common Factor is the largest of those common factors.
For example, since \[1\] , \[2\] , and \[4\] are common factors of both \[12\] and \[16\] , and \[4\] is the greatest of them, the HCF of \[12\] and \[16\] is \[4\] .
Following steps are followed for finding HCF:
Step \[1\] : Find all the factors of the given numbers.
With the help of multiplication table, we can find out that factors are as follows:
For \[10:1,2,5,10\]
For \[100:1,2,4,5,10,20,25,50,100\]
Step \[2\] : Find the common factors of both the numbers:
The common factors are \[1,2,5,10\] .
Step \[3\] : Find the highest common factor from Step \[2\] :
 \[10\] is the highest common factor.
Hence \[10\] is the HCF of \[10\] and \[100\] .
So, the correct answer is “10”.

Note: HCF is also called as “Greatest Common Factor” (GCF). They are useful in solving and simplifying fractions.
We can use alternative method based on prime factorization as follows:
Find the prime factors of both the numbers with the help of division rule-
 \[100 = 10 \times 10 = 2 \times 2 \times 5 \times 5\]
 \[10 = 2 \times 5\]
Now we have to multiply the common factors to find GCF:
 \[2 \times 5 = 10\]
Hence \[10\] is the HCF of \[10\] and \[100\] .