GCF of 64 and 72
GCF of 64 and 72 is the largest possible number that divides 64 and 72 exactly without any remainder. The factors of 64 and 72 are 1, 2, 4, 8, 16, 32, 64 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 64 and 72 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 64 and 72 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 64 and 72?
Answer: GCF of 64 and 72 is 8.
Explanation:
The GCF of two non-zero integers, x(64) and y(72), is the greatest positive integer m(8) that divides both x(64) and y(72) without any remainder.
Methods to Find GCF of 64 and 72
The methods to find the GCF of 64 and 72 are explained below.
- Listing Common Factors
- Using Euclid's Algorithm
- Long Division Method
GCF of 64 and 72 by Listing Common Factors
- Factors of 64: 1, 2, 4, 8, 16, 32, 64
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 4 common factors of 64 and 72, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 64 and 72 is 8.
GCF of 64 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 = 64
- GCF(72, 64) = GCF(64, 72 mod 64) = GCF(64, 8)
- GCF(64, 8) = GCF(8, 64 mod 8) = GCF(8, 0)
- GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 64 and 72 is 8.
GCF of 64 and 72 by Long Division
GCF of 64 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 64 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (64) by the remainder (8).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (8) is the GCF of 64 and 72.
☛ Also Check:
- GCF of 12 and 15 = 3
- GCF of 21 and 35 = 7
- GCF of 10 and 35 = 5
- GCF of 38 and 57 = 19
- GCF of 5 and 10 = 5
- GCF of 6 and 7 = 1
- GCF of 18 and 32 = 2
FAQs on GCF of 64 and 72
What is the GCF of 64 and 72?
The GCF of 64 and 72 is 8. To calculate the GCF (Greatest Common Factor) of 64 and 72, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 64 and 72, i.e., 8.
What is the Relation Between LCM and GCF of 64, 72?
The following equation can be used to express the relation between Least Common Multiple and GCF of 64 and 72, i.e. GCF × LCM = 64 × 72.
How to Find the GCF of 64 and 72 by Long Division Method?
To find the GCF of 64, 72 using long division method, 72 is divided by 64. The corresponding divisor (8) when remainder equals 0 is taken as GCF.
If the GCF of 72 and 64 is 8, Find its LCM.
GCF(72, 64) × LCM(72, 64) = 72 × 64
Since the GCF of 72 and 64 = 8
⇒ 8 × LCM(72, 64) = 4608
Therefore, LCM = 576
☛ GCF Calculator
What are the Methods to Find GCF of 64 and 72?
There are three commonly used methods to find the GCF of 64 and 72.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
How to Find the GCF of 64 and 72 by Prime Factorization?
To find the GCF of 64 and 72, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 64 and 72. Hence, GCF(64, 72) = 2 × 2 × 2 = 8
☛ Prime Number