GCF of 72 and 90
GCF of 72 and 90 is the largest possible number that divides 72 and 90 exactly without any remainder. The factors of 72 and 90 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 72 and 90 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 72 and 90 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 72 and 90?
Answer: GCF of 72 and 90 is 18.
Explanation:
The GCF of two non-zero integers, x(72) and y(90), is the greatest positive integer m(18) that divides both x(72) and y(90) without any remainder.
Methods to Find GCF of 72 and 90
The methods to find the GCF of 72 and 90 are explained below.
- Long Division Method
- Listing Common Factors
- Prime Factorization Method
GCF of 72 and 90 by Long Division
GCF of 72 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 90 (larger number) by 72 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (18).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (18) is the GCF of 72 and 90.
GCF of 72 and 90 by Listing Common Factors
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
There are 6 common factors of 72 and 90, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest common factor of 72 and 90 is 18.
GCF of 72 and 90 by Prime Factorization
Prime factorization of 72 and 90 is (2 × 2 × 2 × 3 × 3) and (2 × 3 × 3 × 5) respectively. As visible, 72 and 90 have common prime factors. Hence, the GCF of 72 and 90 is 2 × 3 × 3 = 18.
☛ Also Check:
- GCF of 12 and 18 = 6
- GCF of 44 and 66 = 22
- GCF of 33 and 44 = 11
- GCF of 92 and 23 = 23
- GCF of 48 and 72 = 24
- GCF of 15 and 24 = 3
- GCF of 5 and 6 = 1
FAQs on GCF of 72 and 90
What is the GCF of 72 and 90?
The GCF of 72 and 90 is 18. To calculate the GCF (Greatest Common Factor) of 72 and 90, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 72 and 90, i.e., 18.
If the GCF of 90 and 72 is 18, Find its LCM.
GCF(90, 72) × LCM(90, 72) = 90 × 72
Since the GCF of 90 and 72 = 18
⇒ 18 × LCM(90, 72) = 6480
Therefore, LCM = 360
☛ GCF Calculator
What are the Methods to Find GCF of 72 and 90?
There are three commonly used methods to find the GCF of 72 and 90.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
How to Find the GCF of 72 and 90 by Long Division Method?
To find the GCF of 72, 90 using long division method, 90 is divided by 72. The corresponding divisor (18) when remainder equals 0 is taken as GCF.
How to Find the GCF of 72 and 90 by Prime Factorization?
To find the GCF of 72 and 90, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 72 and 90. Hence, GCF(72, 90) = 2 × 3 × 3 = 18
☛ Prime Numbers
What is the Relation Between LCM and GCF of 72, 90?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 72 and 90, i.e. GCF × LCM = 72 × 90.