GCF of 40 and 42

GCF of 40 and 42 is the largest possible number that divides 40 and 42 exactly without any remainder. The factors of 40 and 42 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 40 and 42 - prime factorization, long division, and Euclidean algorithm.

Answer: GCF of 40 and 42 is 2.

Explanation:

The GCF of two non-zero integers, x(40) and y(42), is the greatest positive integer m(2) that divides both x(40) and y(42) without any remainder.

The methods to find the GCF of 40 and 42 are explained below.

• Listing Common Factors
• Prime Factorization Method
• Long Division Method

GCF of 40 and 42 by Listing Common Factors

• Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 2 common factors of 40 and 42, that are 1 and 2. Therefore, the greatest common factor of 40 and 42 is 2.

GCF of 40 and 42 by Prime Factorization

Prime factorization of 40 and 42 is (2 × 2 × 2 × 5) and (2 × 3 × 7) respectively. As visible, 40 and 42 have only one common prime factor i.e. 2. Hence, the GCF of 40 and 42 is 2.

GCF of 40 and 42 by Long Division

GCF of 40 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 40 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (40) by the remainder (2).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 40 and 42.

☛ Also Check:

• GCF of 30 and 50 = 10
• GCF of 20 and 35 = 5
• GCF of 18 and 28 = 2
• GCF of 45 and 63 = 9
• GCF of 32 and 40 = 8
• GCF of 3 and 12 = 3
• GCF of 72 and 84 = 12

FAQs on GCF of 40 and 42

What is the GCF of 40 and 42?

The GCF of 40 and 42 is 2. To calculate the greatest common factor of 40 and 42, we need to factor each number (factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 40 and 42, i.e., 2.

How to Find the GCF of 40 and 42 by Long Division Method?

To find the GCF of 40, 42 using long division method, 42 is divided by 40. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

How to Find the GCF of 40 and 42 by Prime Factorization?

To find the GCF of 40 and 42, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 42 = 2 × 3 × 7.
⇒ Since 2 is the only common prime factor of 40 and 42. Hence, GCF (40, 42) = 2.
☛ Prime Numbers

If the GCF of 42 and 40 is 2, Find its LCM.

GCF(42, 40) × LCM(42, 40) = 42 × 40
Since the GCF of 42 and 40 = 2
⇒ 2 × LCM(42, 40) = 1680
Therefore, LCM = 840
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 40 and 42?

There are three commonly used methods to find the GCF of 40 and 42.

• By Euclidean Algorithm
• By Long Division
• By Prime Factorization

What is the Relation Between LCM and GCF of 40, 42?

The following equation can be used to express the relation between LCM and GCF of 40 and 42, i.e. GCF × LCM = 40 × 42.