GCF of 72 and 80
GCF of 72 and 80 is the largest possible number that divides 72 and 80 exactly without any remainder. The factors of 72 and 80 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the GCF of 72 and 80 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 72 and 80 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 72 and 80?
Answer: GCF of 72 and 80 is 8.
Explanation:
The GCF of two non-zero integers, x(72) and y(80), is the greatest positive integer m(8) that divides both x(72) and y(80) without any remainder.
Methods to Find GCF of 72 and 80
Let's look at the different methods for finding the GCF of 72 and 80.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 72 and 80 by Long Division
GCF of 72 and 80 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 80 (larger number) by 72 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (8).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (8) is the GCF of 72 and 80.
GCF of 72 and 80 by Prime Factorization
Prime factorization of 72 and 80 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 5) respectively. As visible, 72 and 80 have common prime factors. Hence, the GCF of 72 and 80 is 2 × 2 × 2 = 8.
GCF of 72 and 80 by Listing Common Factors
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
There are 4 common factors of 72 and 80, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 72 and 80 is 8.
☛ Also Check:
- GCF of 38 and 57 = 19
- GCF of 12 and 56 = 4
- GCF of 28 and 63 = 7
- GCF of 45 and 81 = 9
- GCF of 39 and 65 = 13
- GCF of 9 and 21 = 3
- GCF of 6 and 10 = 2
FAQs on GCF of 72 and 80
What is the GCF of 72 and 80?
The GCF of 72 and 80 is 8. To calculate the greatest common factor (GCF) of 72 and 80, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 72 and 80, i.e., 8.
What is the Relation Between LCM and GCF of 72, 80?
The following equation can be used to express the relation between LCM and GCF of 72 and 80, i.e. GCF × LCM = 72 × 80.
What are the Methods to Find GCF of 72 and 80?
There are three commonly used methods to find the GCF of 72 and 80.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
If the GCF of 80 and 72 is 8, Find its LCM.
GCF(80, 72) × LCM(80, 72) = 80 × 72
Since the GCF of 80 and 72 = 8
⇒ 8 × LCM(80, 72) = 5760
Therefore, LCM = 720
☛ GCF Calculator
How to Find the GCF of 72 and 80 by Prime Factorization?
To find the GCF of 72 and 80, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 72 and 80. Hence, GCF(72, 80) = 2 × 2 × 2 = 8
☛ What is a Prime Number?
How to Find the GCF of 72 and 80 by Long Division Method?
To find the GCF of 72, 80 using long division method, 80 is divided by 72. The corresponding divisor (8) when remainder equals 0 is taken as GCF.