Question

Find the greatest common factor of 42,126 and 210.
A.2
B.6
C.14
D.21
E.42

Answer 1

Hint: Here first we understand the meaning of greatest common factor, the greatest common factor defined by the set of numbers. To find the greatest common factor of three numbers, it means list out the prime factors of each number. After that multiply those numbers which is common in prime factors.

Complete step-by-step answer:
From the given data, the factors are 42,126 and 210.
Now, we calculate the greatest common factor by the use of above given information.
Now, we first calculate the prime factors of the given factors that are 42,126 and 210.
The prime factor of 42 or 42 can be divided by 2,3, and 7.
The prime factor of 126 or 126 can be divided by 2,3, 3, and 7.
The prime factor of 210 or 210 can be divided by 2,3, 5, and 7.
Therefore, we take the common values from the prime factors 42, 126, and 210 are 2,3,7. That means the greatest common value is the multiplication of the common values by the definition. That is:
$2\times 3\times 7=42$
Hence, the greatest common factor value is 42. The option (E) is the correct option that is 42.

Note: Here we should know the prime numbers. Prime numbers are the numbers which can be divided by itself and by 1. The prime numbers are $2,3,5,7,11,13,17,...$. Factors means the numbers which are divided by other numbers may be exactly and without leaving any remainder.