GCF of 72 and 108
GCF of 72 and 108 is the largest possible number that divides 72 and 108 exactly without any remainder. The factors of 72 and 108 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 respectively. There are 3 commonly used methods to find the GCF of 72 and 108 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 72 and 108 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 72 and 108?
Answer: GCF of 72 and 108 is 36.
Explanation:
The GCF of two non-zero integers, x(72) and y(108), is the greatest positive integer m(36) that divides both x(72) and y(108) without any remainder.
Methods to Find GCF of 72 and 108
Let's look at the different methods for finding the GCF of 72 and 108.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 72 and 108 by Listing Common Factors
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
There are 9 common factors of 72 and 108, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the greatest common factor of 72 and 108 is 36.
GCF of 72 and 108 by Long Division
GCF of 72 and 108 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 108 (larger number) by 72 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (36).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (36) is the GCF of 72 and 108.
GCF of 72 and 108 by Prime Factorization
Prime factorization of 72 and 108 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 3 × 3 × 3) respectively. As visible, 72 and 108 have common prime factors. Hence, the GCF of 72 and 108 is 2 × 2 × 3 × 3 = 36.
☛ Also Check:
- GCF of 42 and 72 = 6
- GCF of 60 and 75 = 15
- GCF of 20 and 45 = 5
- GCF of 26 and 65 = 13
- GCF of 42 and 90 = 6
- GCF of 35 and 50 = 5
- GCF of 16 and 28 = 4
FAQs on GCF of 72 and 108
What is the GCF of 72 and 108?
The GCF of 72 and 108 is 36. To calculate the greatest common factor of 72 and 108, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108) and choose the greatest factor that exactly divides both 72 and 108, i.e., 36.
What are the Methods to Find GCF of 72 and 108?
There are three commonly used methods to find the GCF of 72 and 108.
- By Listing Common Factors
- By Prime Factorization
- By Long Division
How to Find the GCF of 72 and 108 by Prime Factorization?
To find the GCF of 72 and 108, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 108 = 2 × 2 × 3 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 72 and 108. Hence, GCF(72, 108) = 2 × 2 × 3 × 3 = 36
☛ Prime Numbers
If the GCF of 108 and 72 is 36, Find its LCM.
GCF(108, 72) × LCM(108, 72) = 108 × 72
Since the GCF of 108 and 72 = 36
⇒ 36 × LCM(108, 72) = 7776
Therefore, LCM = 216
☛ GCF Calculator
What is the Relation Between LCM and GCF of 72, 108?
The following equation can be used to express the relation between LCM and GCF of 72 and 108, i.e. GCF × LCM = 72 × 108.
How to Find the GCF of 72 and 108 by Long Division Method?
To find the GCF of 72, 108 using long division method, 108 is divided by 72. The corresponding divisor (36) when remainder equals 0 is taken as GCF.