Question

What is GCF of 35 and 49?

Answer 1

Hint: We need to find the GCF of 35 and 49. First we need to find the common factors of 35 and 49 from their factors’ list. Then we find the greatest common factor of 35 and 49. We can also take the simultaneous factorisation of those two numbers to find the GCF.

Complete step-by-step answer:
We need to find the GCF of 49 and 35. GCF stands for greatest common factor.
we first find the factors for 35 and 49.
The factors of 35 are $1,5,7,35$ . The factors of 49 are $1,7,7,49$ .
The common factors of 35 and 49 are $1,7$ .
The greatest common factor of 35 and 49 is $7$ .
We also can use the simultaneous factorisation to find the greatest common factor of 35 and 49.
We have to divide both of them with possible primes which can divide both of them.
$$\begin{array}{rl}& 7|\underset{―}{35,49}\\ & 1|\underset{―}{5,7}\end{array}$$
The only possible prime being 7. Therefore, the greatest common factor of 35 and 49 is 7.
So, the correct answer is “7”.

Note: We need to remember that the GCF has to be only one number. It is the greatest possible divisor of all the given numbers. If the given numbers are prime numbers, then the GCD of those numbers will always be 1.
Therefore, if for numbers $x$ and $y$ , the GCD is $a$ then the GCD of the numbers ${\displaystyle \frac{x}{a}}$ and ${\displaystyle \frac{y}{a}}$ will be 1.