GCF of 72 and 36 is the largest possible number that divides 72 and 36 exactly without any remainder. The factors of 72 and 36 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 72 and 36 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 72 and 36 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 72 and 36?
Answer: GCF of 72 and 36 is 36.
Explanation:
The GCF of two non-zero integers, x(72) and y(36), is the greatest positive integer m(36) that divides both x(72) and y(36) without any remainder.
Methods to Find GCF of 72 and 36
The methods to find the GCF of 72 and 36 are explained below.
- Long Division Method
- Prime Factorization Method
- Using Euclid's Algorithm
GCF of 72 and 36 by Long Division
GCF of 72 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 72 (larger number) by 36 (smaller number).
- Step 2: Since the remainder = 0, the divisor (36) is the GCF of 72 and 36.
The corresponding divisor (36) is the GCF of 72 and 36.
GCF of 72 and 36 by Prime Factorization
Prime factorization of 72 and 36 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 72 and 36 have common prime factors. Hence, the GCF of 72 and 36 is 2 × 2 × 3 × 3 = 36.
GCF of 72 and 36 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 = 36
- GCF(72, 36) = GCF(36, 72 mod 36) = GCF(36, 0)
- GCF(36, 0) = 36 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 72 and 36 is 36.
☛ Also Check:
- GCF of 36 and 90 = 18
- GCF of 45 and 105 = 15
- GCF of 45 and 60 = 15
- GCF of 18 and 81 = 9
- GCF of 11 and 44 = 11
- GCF of 8 and 9 = 1
- GCF of 25 and 60 = 5
GCF of 72 and 36 Examples
Example 1: Find the GCF of 72 and 36, if their LCM is 72.
Solution:
∵ LCM × GCF = 72 × 36
⇒ GCF(72, 36) = (72 × 36)/72 = 36
Therefore, the greatest common factor of 72 and 36 is 36.Example 2: The product of two numbers is 2592. If their GCF is 36, what is their LCM?
Solution:
Given: GCF = 36 and product of numbers = 2592
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2592/36
Therefore, the LCM is 72.Example 3: For two numbers, GCF = 36 and LCM = 72. If one number is 72, find the other number.
Solution:
Given: GCF (x, 72) = 36 and LCM (x, 72) = 72
∵ GCF × LCM = 72 × (x)
⇒ x = (GCF × LCM)/72
⇒ x = (36 × 72)/72
⇒ x = 36
Therefore, the other number is 36.
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FAQs on GCF of 72 and 36
What is the GCF of 72 and 36?
The GCF of 72 and 36 is 36. To calculate the greatest common factor (GCF) of 72 and 36, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 72 and 36, i.e., 36.
What is the Relation Between LCM and GCF of 72, 36?
The following equation can be used to express the relation between LCM and GCF of 72 and 36, i.e. GCF × LCM = 72 × 36.
What are the Methods to Find GCF of 72 and 36?
There are three commonly used methods to find the GCF of 72 and 36.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
How to Find the GCF of 72 and 36 by Long Division Method?
To find the GCF of 72, 36 using long division method, 72 is divided by 36. The corresponding divisor (36) when remainder equals 0 is taken as GCF.
If the GCF of 36 and 72 is 36, Find its LCM.
GCF(36, 72) × LCM(36, 72) = 36 × 72
Since the GCF of 36 and 72 = 36
⇒ 36 × LCM(36, 72) = 2592
Therefore, LCM = 72
☛ GCF Calculator
How to Find the GCF of 72 and 36 by Prime Factorization?
To find the GCF of 72 and 36, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 72 and 36. Hence, GCF(72, 36) = 2 × 2 × 3 × 3 = 36
☛ What is a Prime Number?
