Find the largest whole number which is a factor of both 101 and 42.

Alyce Wilkinson

Alyce Wilkinson

Answered question

2021-04-20

Find the largest whole number which is a factor of both 101 and 42.

Answer & Explanation

falhiblesw

falhiblesw

Skilled2021-04-22Added 97 answers

Step 1
We are required to find the greatest common divisor (also known as the highest common factor or HCF) of 101 and 42.
The prime factorization method to find the HCF of two numbers m and n is as follows.
Express each one of the given numbers as a product of prime numbers.
The product of the least powers of common prime factor gives HCF.
Step 2
The prime factorization of 101 is
101=101
Note that this is so since 101 is a prime number
The prime factorization of 42 is
42=2×3×7
Note that there are no common prime factors between 101 and 42.
Hence, the HCF of 101 and 42 is 1, i.e. the largest whole number which is a factor of both 101 and 42 is 1.
Note that when one of the numbers is prime, the HCF is always equal to 1.

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