Question

Find the GCD of \[42\] and \[56\].

Answer 1

Hint:
The greatest common divisor is the largest integer that divides the two numbers.

Complete step by step solution:
To find the greatest common factor, the largest integer that divides both the numbers needs to be found.
Find the prime factors of \[42\]:
\[42 = 2 \times 3 \times 7\]
Find the prime factors of \[56\]:
\[56 = 2 \times 2 \times 2 \times 7\]
To find the GCD of \[42\] and \[56\] multiply all the prime factors that are common to both the numbers:
The common prime factors of \[42\] and \[56\] are \[2\] and \[7\]

Therefore the GCD of \[42\] and \[56\] is:
\[2 \times 7\] \[ = \] \[14\].

Additional information:
1) Any number which can only be divided by \[1\] and itself is a prime number.
2) A number \[a\] is said to be a factor of a number \[b\] if \[a\] divides \[b\] completely without leaving any remainder.

Note:
The GCD of two numbers can also be found in the following manner:
1) Divide the larger number with the smaller number, thus a quotient and a remainder are obtained.
2) If the remainder is \[0\] then the smaller number is the greatest common divisor, otherwise, repeat the above step with the remainder and the smaller number.
3) Here if \[56\] is divided by \[42\] then the quotient is \[1\] and the remainder is \[14\]. Since the remainder is not zero again divide\[42\] by \[14\], now the quotient is \[3\] and the remainder is \[0\]. Hence \[14\] is the greatest common factor of \[42\] and \[56\].