GCF of 105 and 42

What is the GCF of 105 and 42?

GCF of 105 and 42

is 21

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Greatest Common Factor

What is the Greatest Common Factor of 105 and 42? The greatest common factor (GCF) of a set of numbers is the largest positive integer that divides each of the numbers evenly. It's also called the greatest common divisor (GCD).

The GCF can be found using a variety of methods, including prime factorization and division. The Euclidean algorithm is a commonly used method for finding the GCF of two numbers, and it can be extended to finding the GCF of more than two numbers.

To find GCF (Greatest Common Factor) between two numbers, mainly there are two methods available, Those are-

1. Prime Factorization Method: Find the prime factors of both number and then multiply of all the common prime factors value, you will get the GCF value.

2. Factors Method: Find the factors of both number. In those both factors the highest common factor number is the GCF value.

For calculation, here's how to calculate GCF of 105 and 42 using those formula above, step by step instructions are given below

Prime Factorization Method:

  1. Find the prime factors of the first number 105.
    3, 5, 7
  2. Find the prime factors of the second number 42.
    2, 3, 7
  3. Multiply of all the common prime factors is the GCF value. Which is,
    21

Factors Method:

  1. Find the factors of the first number 105.
    1, 3, 5, 7, 15, 21, 35, 105
  2. Find the factors of the second number 42.
    1, 2, 3, 6, 7, 14, 21, 42
  3. The biggest common factor number is the GCF value. Which is,
    21

GCF (Greatest Common Factor) of 105 and 42 is 21.

GCD (Greatest Common Divisor) of 105 and 42 is 21.

HCF (Highest Common Factor) of 105 and 42 is 21.

Number GCF LCM
105 & 37 1 3885
105 & 38 1 3990
105 & 39 3 1365
105 & 40 5 840
105 & 41 1 4305
105 & 42 21 210
105 & 43 1 4515
105 & 44 1 4620
105 & 45 15 315
105 & 46 1 4830
105 & 47 1 4935
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