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GCF of 40 and 72

GCF of 40 and 72 is the largest possible number that divides 40 and 72 exactly without any remainder. The factors of 40 and 72 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 40 and 72 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 40 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 40 and 72?

Answer: GCF of 40 and 72 is 8.

Explanation:

The GCF of two non-zero integers, x(40) and y(72), is the greatest positive integer m(8) that divides both x(40) and y(72) without any remainder.

Methods to Find GCF of 40 and 72

Let's look at the different methods for finding the GCF of 40 and 72.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 40 and 72 by Prime Factorization

Prime factorization of 40 and 72 is (2 × 2 × 2 × 5) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 40 and 72 have common prime factors. Hence, the GCF of 40 and 72 is 2 × 2 × 2 = 8.

GCF of 40 and 72 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 = 72 and Y = 40

GCF(72, 40) = GCF(40, 72 mod 40) = GCF(40, 32)
GCF(40, 32) = GCF(32, 40 mod 32) = GCF(32, 8)
GCF(32, 8) = GCF(8, 32 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 40 and 72 is 8.

GCF of 40 and 72 by Long Division

GCF of 40 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 72 (larger number) by 40 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (40) by the remainder (32).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 40 and 72.

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GCF of 40 and 72 Examples

Example 1: Find the greatest number that divides 40 and 72 exactly.

Solution:

The greatest number that divides 40 and 72 exactly is their greatest common factor, i.e. GCF of 40 and 72.
⇒ Factors of 40 and 72:
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 40 and 72 is 8.
Example 2: For two numbers, GCF = 8 and LCM = 360. If one number is 72, find the other number.

Solution:

Given: GCF (y, 72) = 8 and LCM (y, 72) = 360
∵ GCF × LCM = 72 × (y)
⇒ y = (GCF × LCM)/72
⇒ y = (8 × 360)/72
⇒ y = 40
Therefore, the other number is 40.
Example 3: The product of two numbers is 2880. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 2880
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2880/8
Therefore, the LCM is 360.

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FAQs on GCF of 40 and 72

What is the GCF of 40 and 72?

The GCF of 40 and 72 is 8. To calculate the GCF (Greatest Common Factor) of 40 and 72, we need to factor each number (factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 40 and 72, i.e., 8.

What is the Relation Between LCM and GCF of 40, 72?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 40 and 72, i.e. GCF × LCM = 40 × 72.

What are the Methods to Find GCF of 40 and 72?

There are three commonly used methods to find the GCF of 40 and 72.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 72 and 40 is 8, Find its LCM.

GCF(72, 40) × LCM(72, 40) = 72 × 40
Since the GCF of 72 and 40 = 8
⇒ 8 × LCM(72, 40) = 2880
Therefore, LCM = 360
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How to Find the GCF of 40 and 72 by Prime Factorization?

To find the GCF of 40 and 72, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 40 and 72. Hence, GCF(40, 72) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

How to Find the GCF of 40 and 72 by Long Division Method?

To find the GCF of 40, 72 using long division method, 72 is divided by 40. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

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