greates common factor of 28 and 42 using prime factorization
To find the greatest common factor of 28 and 42 using prime factorization, we need to first find the prime factorization of both numbers.
The prime factorization of 28 is: 2 * 2 * 7 = 2^2 * 7
The prime factorization of 42 is: 2 * 3 * 7
Now, we look for the common prime factors:
The common prime factors are 2 and 7. However, we take the lowest power of each prime factor between the two numbers. So, the greatest common factor is 2 * 7 = 14.
Therefore, the greatest common factor of 28 and 42 is 14.
To find the greatest common factor (GCF) of 28 and 42 using prime factorization, you need to decompose both numbers into their prime factors.
Step 1: Prime factorization of 28
The prime factors of 28 are 2 and 7. To find this, you can start by dividing 28 by the smallest prime number (2). After dividing, you get 14. Then, divide 14 by 2 to get 7. Therefore, the prime factorization of 28 is 2^2 × 7.
Step 2: Prime factorization of 42
The prime factors of 42 are 2, 3, and 7. To find this, you can start by dividing 42 by the smallest prime number (2). After dividing, you get 21. Then, divide 21 by 3 to get 7. Therefore, the prime factorization of 42 is 2 × 3 × 7.
Step 3: Determine the common factors
To find the GCF, you need to figure out the factors that are common to both 28 and 42. From their prime factorizations, the only prime factor they have in common is 7.
Step 4: Calculate the GCF
To calculate the GCF, you multiply the common factors: GCF = 7.
Therefore, the greatest common factor of 28 and 42, using prime factorization, is 7.