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GCF of 32 and 42

GCF of 32 and 42 is the largest possible number that divides 32 and 42 exactly without any remainder. The factors of 32 and 42 are 1, 2, 4, 8, 16, 32 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 32 and 42 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 32 and 42
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 42?

Answer: GCF of 32 and 42 is 2.

Explanation:

The GCF of two non-zero integers, x(32) and y(42), is the greatest positive integer m(2) that divides both x(32) and y(42) without any remainder.

Methods to Find GCF of 32 and 42

Let's look at the different methods for finding the GCF of 32 and 42.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 32 and 42 by Long Division

GCF of 32 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 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 32 and 42.

GCF of 32 and 42 by Listing Common Factors

Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 2 common factors of 32 and 42, that are 1 and 2. Therefore, the greatest common factor of 32 and 42 is 2.

GCF of 32 and 42 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 = 42 and Y = 32

GCF(42, 32) = GCF(32, 42 mod 32) = GCF(32, 10)
GCF(32, 10) = GCF(10, 32 mod 10) = GCF(10, 2)
GCF(10, 2) = GCF(2, 10 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 32 and 42 is 2.

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GCF of 32 and 42 Examples

Example 1: For two numbers, GCF = 2 and LCM = 672. If one number is 32, find the other number.

Solution:

Given: GCF (z, 32) = 2 and LCM (z, 32) = 672
∵ GCF × LCM = 32 × (z)
⇒ z = (GCF × LCM)/32
⇒ z = (2 × 672)/32
⇒ z = 42
Therefore, the other number is 42.
Example 2: Find the greatest number that divides 32 and 42 exactly.

Solution:

The greatest number that divides 32 and 42 exactly is their greatest common factor, i.e. GCF of 32 and 42.
⇒ Factors of 32 and 42:
- Factors of 32 = 1, 2, 4, 8, 16, 32
- Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Therefore, the GCF of 32 and 42 is 2.
Example 3: Find the GCF of 32 and 42, if their LCM is 672.

Solution:

∵ LCM × GCF = 32 × 42
⇒ GCF(32, 42) = (32 × 42)/672 = 2
Therefore, the greatest common factor of 32 and 42 is 2.

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FAQs on GCF of 32 and 42

What is the GCF of 32 and 42?

The GCF of 32 and 42 is 2. To calculate the greatest common factor (GCF) of 32 and 42, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 32 and 42, i.e., 2.

If the GCF of 42 and 32 is 2, Find its LCM.

GCF(42, 32) × LCM(42, 32) = 42 × 32
Since the GCF of 42 and 32 = 2
⇒ 2 × LCM(42, 32) = 1344
Therefore, LCM = 672
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How to Find the GCF of 32 and 42 by Long Division Method?

To find the GCF of 32, 42 using long division method, 42 is divided by 32. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 32 and 42?

There are three commonly used methods to find the GCF of 32 and 42.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 32, 42?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 32 and 42, i.e. GCF × LCM = 32 × 42.

How to Find the GCF of 32 and 42 by Prime Factorization?

To find the GCF of 32 and 42, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 42 = 2 × 3 × 7.
⇒ Since 2 is the only common prime factor of 32 and 42. Hence, GCF (32, 42) = 2.
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