Find the greatest number that is divisible by 42 and 56 by leaving no reminder. Find prime factorization of that number
Answers
GCF of 42 and 56
add
GCF of 42 and 56 is the largest possible number that divides 42 and 56 exactly without any remainder. The factors of 42 and 56 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 42 and 56 - prime factorization, Euclidean algorithm, and long division.
What is GCF of 42 and 56?
Answer: GCF of 42 and 56 is 14.
GCF of 42 and 56
Explanation:
The GCF of two non-zero integers, x(42) and y(56), is the greatest positive integer m(14) that divides both x(42) and y(56) without any remainder.
Methods to Find GCF of 42 and 56
The methods to find the GCF of 42 and 56 are explained below.
Listing Common Factors
Long Division Method
Prime Factorization Method
GCF of 42 and 56 by Listing Common Factors
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
There are 4 common factors of 42 and 56, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 42 and 56 is 14.
GCF of 42 and 56 by Long Division
GCF of 42 and 56 by Long Division
GCF of 42 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
Step 1: Divide 56 (larger number) by 42 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (14).
Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (14) is the GCF of 42 and 56.
GCF of 42 and 56 by Prime Factorization
GCF of 42 and 56 by Prime Factorization
Prime factorization of 42 and 56 is (2 × 3 × 7) and (2 × 2 × 2 × 7) respectively. As visible, 42 and 56 have common prime factors. Hence, the GCF of 42 and 56 is 2 × 7 = 14.
I hope it helps
please mark this the brainliest answer