GCF of 72 and 96
GCF of 72 and 96 is the largest possible number that divides 72 and 96 exactly without any remainder. The factors of 72 and 96 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the GCF of 72 and 96 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 72 and 96 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 72 and 96?
Answer: GCF of 72 and 96 is 24.
Explanation:
The GCF of two non-zero integers, x(72) and y(96), is the greatest positive integer m(24) that divides both x(72) and y(96) without any remainder.
Methods to Find GCF of 72 and 96
Let's look at the different methods for finding the GCF of 72 and 96.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
GCF of 72 and 96 by Prime Factorization
Prime factorization of 72 and 96 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 72 and 96 have common prime factors. Hence, the GCF of 72 and 96 is 2 × 2 × 2 × 3 = 24.
GCF of 72 and 96 by Listing Common Factors
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
There are 8 common factors of 72 and 96, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 72 and 96 is 24.
GCF of 72 and 96 by Long Division
GCF of 72 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 96 (larger number) by 72 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (24).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (24) is the GCF of 72 and 96.
☛ Also Check:
- GCF of 49 and 98 = 49
- GCF of 12 and 60 = 12
- GCF of 9 and 16 = 1
- GCF of 7 and 56 = 7
- GCF of 6 and 36 = 6
- GCF of 18 and 30 = 6
- GCF of 3 and 9 = 3
FAQs on GCF of 72 and 96
What is the GCF of 72 and 96?
The GCF of 72 and 96 is 24. To calculate the GCF of 72 and 96, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the greatest factor that exactly divides both 72 and 96, i.e., 24.
How to Find the GCF of 72 and 96 by Prime Factorization?
To find the GCF of 72 and 96, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 72 and 96. Hence, GCF(72, 96) = 2 × 2 × 2 × 3 = 24
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 72, 96?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 72 and 96, i.e. GCF × LCM = 72 × 96.
If the GCF of 96 and 72 is 24, Find its LCM.
GCF(96, 72) × LCM(96, 72) = 96 × 72
Since the GCF of 96 and 72 = 24
⇒ 24 × LCM(96, 72) = 6912
Therefore, LCM = 288
☛ GCF Calculator
What are the Methods to Find GCF of 72 and 96?
There are three commonly used methods to find the GCF of 72 and 96.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 72 and 96 by Long Division Method?
To find the GCF of 72, 96 using long division method, 96 is divided by 72. The corresponding divisor (24) when remainder equals 0 is taken as GCF.