Find the GCF of 42 and 28
The greatest common factor (GCF) of 42 and 28 is 14.
To find the greatest common factor (GCF) of 42 and 28, we can use the following steps:
Step 1: List the factors of each number.
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 28: 1, 2, 4, 7, 14, 28
Step 2: Identify the common factors of both numbers.
Common factors of 42 and 28: 1, 2, 7, 14
Step 3: Determine the largest common factor, which is the GCF.
GCF of 42 and 28: 14
Therefore, the greatest common factor (GCF) of 42 and 28 is 14.
To find the Greatest Common Factor (GCF) of two numbers, we can use the method of prime factorization.
Step 1: Prime Factorization of 42
To find the prime factorization of 42, we need to find the prime numbers that divide evenly into 42. We start by dividing 42 by the smallest prime number, which is 2. Since 42 is an even number, it is divisible by 2. So, we divide 42 by 2, which gives us 21.
21 is not divisible by 2, so we move on to the next prime number, which is 3. Since 21 is divisible by 3, we divide 21 by 3, resulting in 7.
7 is a prime number, so we have completed the prime factorization of 42: 2 x 3 x 7.
Step 2: Prime Factorization of 28
Similarly, we find the prime factorization of 28. We divide 28 by 2, which gives us 14. We continue dividing by 2 until we can no longer divide evenly.
The prime factorization of 28 is 2 x 2 x 7.
Step 3: Finding the GCF
To find the GCF, we look for the common prime factors between the two numbers. In this case, both 42 and 28 have the prime factor 2 and 7.
To get the GCF, we multiply the common prime factors: 2 x 7 = 14.
Therefore, the GCF of 42 and 28 is 14.