GCF of 36 and 42
GCF of 36 and 42 is the largest possible number that divides 36 and 42 exactly without any remainder. The factors of 36 and 42 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 36 and 42  long division, prime factorization, and Euclidean algorithm.
1.  GCF of 36 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 36 and 42?
Answer: GCF of 36 and 42 is 6.
Explanation:
The GCF of two nonzero integers, x(36) and y(42), is the greatest positive integer m(6) that divides both x(36) and y(42) without any remainder.
Methods to Find GCF of 36 and 42
The methods to find the GCF of 36 and 42 are explained below.
 Long Division Method
 Listing Common Factors
 Prime Factorization Method
GCF of 36 and 42 by Long Division
GCF of 36 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 42 (larger number) by 36 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (6).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 36 and 42.
GCF of 36 and 42 by Listing Common Factors
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 36 and 42, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 36 and 42 is 6.
GCF of 36 and 42 by Prime Factorization
Prime factorization of 36 and 42 is (2 × 2 × 3 × 3) and (2 × 3 × 7) respectively. As visible, 36 and 42 have common prime factors. Hence, the GCF of 36 and 42 is 2 × 3 = 6.
☛ Also Check:
 GCF of 2 and 6 = 2
 GCF of 28 and 12 = 4
 GCF of 24 and 72 = 24
 GCF of 12 and 36 = 12
 GCF of 63 and 84 = 21
 GCF of 12 and 42 = 6
 GCF of 8 and 20 = 4
GCF of 36 and 42 Examples

Example 1: Find the GCF of 36 and 42, if their LCM is 252.
Solution:
∵ LCM × GCF = 36 × 42
⇒ GCF(36, 42) = (36 × 42)/252 = 6
Therefore, the greatest common factor of 36 and 42 is 6. 
Example 2: Find the greatest number that divides 36 and 42 exactly.
Solution:
The greatest number that divides 36 and 42 exactly is their greatest common factor, i.e. GCF of 36 and 42.
⇒ Factors of 36 and 42: Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Therefore, the GCF of 36 and 42 is 6.

Example 3: The product of two numbers is 1512. If their GCF is 6, what is their LCM?
Solution:
Given: GCF = 6 and product of numbers = 1512
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1512/6
Therefore, the LCM is 252.
FAQs on GCF of 36 and 42
What is the GCF of 36 and 42?
The GCF of 36 and 42 is 6. To calculate the GCF of 36 and 42, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 36 and 42, i.e., 6.
What are the Methods to Find GCF of 36 and 42?
There are three commonly used methods to find the GCF of 36 and 42.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
How to Find the GCF of 36 and 42 by Prime Factorization?
To find the GCF of 36 and 42, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 36 and 42. Hence, GCF(36, 42) = 2 × 3 = 6
☛ Prime Numbers
How to Find the GCF of 36 and 42 by Long Division Method?
To find the GCF of 36, 42 using long division method, 42 is divided by 36. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
If the GCF of 42 and 36 is 6, Find its LCM.
GCF(42, 36) × LCM(42, 36) = 42 × 36
Since the GCF of 42 and 36 = 6
⇒ 6 × LCM(42, 36) = 1512
Therefore, LCM = 252
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 36, 42?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 36 and 42, i.e. GCF × LCM = 36 × 42.
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