GCF of 42 and 90

GCF of 42 and 90 is the largest possible number that divides 42 and 90 exactly without any remainder. The factors of 42 and 90 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 42 and 90 - Euclidean algorithm, prime factorization, and long division.

Answer: GCF of 42 and 90 is 6.

Explanation:

The GCF of two non-zero integers, x(42) and y(90), is the greatest positive integer m(6) that divides both x(42) and y(90) without any remainder.

Let's look at the different methods for finding the GCF of 42 and 90.

• Using Euclid's Algorithm
• Long Division Method
• Listing Common Factors

GCF of 42 and 90 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 90 and Y = 42

• GCF(90, 42) = GCF(42, 90 mod 42) = GCF(42, 6)
• GCF(42, 6) = GCF(6, 42 mod 6) = GCF(6, 0)
• GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 42 and 90 is 6.

GCF of 42 and 90 by Long Division

GCF of 42 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 90 (larger number) by 42 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (6).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 42 and 90.

GCF of 42 and 90 by Listing Common Factors

• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
• Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 42 and 90, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 42 and 90 is 6.

☛ Also Check:

• GCF of 18 and 36 = 18
• GCF of 30 and 48 = 6
• GCF of 15 and 18 = 3
• GCF of 30 and 75 = 15
• GCF of 84 and 42 = 42
• GCF of 36 and 48 = 12
• GCF of 16 and 48 = 16

FAQs on GCF of 42 and 90

What is the GCF of 42 and 90?

The GCF of 42 and 90 is 6. To calculate the greatest common factor (GCF) of 42 and 90, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 42 and 90, i.e., 6.

What are the Methods to Find GCF of 42 and 90?

There are three commonly used methods to find the GCF of 42 and 90.

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

How to Find the GCF of 42 and 90 by Prime Factorization?

To find the GCF of 42 and 90, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 42 and 90. Hence, GCF(42, 90) = 2 × 3 = 6
☛ What is a Prime Number?

How to Find the GCF of 42 and 90 by Long Division Method?

To find the GCF of 42, 90 using long division method, 90 is divided by 42. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

If the GCF of 90 and 42 is 6, Find its LCM.

GCF(90, 42) × LCM(90, 42) = 90 × 42
Since the GCF of 90 and 42 = 6
⇒ 6 × LCM(90, 42) = 3780
Therefore, LCM = 630
☛ GCF Calculator

What is the Relation Between LCM and GCF of 42, 90?

The following equation can be used to express the relation between Least Common Multiple and GCF of 42 and 90, i.e. GCF × LCM = 42 × 90.