Question

Find the GCF of $30,\;60.$

Answer 1

GCF: Greatest Common factor: It’s the greatest number which is a factor of both of them. In simple words it can be described as the largest positive number that divides evenly both the numbers and thus gives a zero remainder. So using the above concept of GCF we can find GCF of $30,\ 60$by first finding the prime factorization of both the numbers $30\;\;{\text{and}}\;\;{\text{20}}$and then multiplying the prime factors which are both common to them.

Complete step by step solution:
Given
$30\;\;{\text{and}}\;\;60...............................\left( i \right)$

Now we know we have to do prime factorization of both the
numbers$30\;\;{\text{and}}\;\;{\text{20}}$.

Prime factorization: It’s the process where the original given number is expressed as the product of prime numbers.

So prime factorization of $30$:
$30 = 2 \times 3 \times 5.......................\left( {ii} \right)$

Prime factorization of 60:
$60 = 2 \times 2 \times 3 \times 5.....................\left( {iii} \right)$

Now we have to multiply the prime factors common to both the numbers, i.e. we have to compare (ii) and (iii) and find the common prime terms and then multiply them.
$\Rightarrow {\text{common}}\;{\text{terms = 2,3,5}}$

Now in order to get the GCF we have to multiply the common terms with each other.
Such that:
${\text{GCF = 2}} \times 3 \times 5 \\\ {\text{GCF = 30}}..............\left( {iv} \right) \\\$
Therefore from (iv) we can write that the GCF of $30,\ 60$ is $30$.

Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. The above question can also be done by simply listing all the possible factors of both the given numbers and then taking the greatest common factor by just comparing the list of factors to find the common factors and choosing the greatest factor among it.