Question

What is GCF of \[30\] and \[42\] ?

Answer 1

Hint: GCF stands for Greatest 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 integer’s i.e exactly. We can use the multiplication table and division rules to find the 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 GCF of \[12\] and \[16\] is \[4\] .
Following steps are followed for finding GCM:
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 \[30:1,2,3,5,6,10,15,30\]
For \[42:1,2,3,6,7,14,21,42\]
Step 2: Find the common factors of both the numbers:
Here \[1,2,3\] and \[6\] are the common factors.
Step 3: Find the greatest common factor from Step 2:
 \[6\] is the greatest common factor.
Hence, the GCF of \[30\] and \[42\] is \[6\] .
So, the correct answer is “6”.

Note: GCF is also called as “Highest Common Factor” (HCF). 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-
 \[30 = 2 \times 3 \times 5\]
 \[42 = 2 \times 3 \times 7\]
Now we have to multiply the common factors to find GCF:
 \[2 \times 3 = 6\]
Hence, the GCF of \[30\] and \[42\] is \[6\] .