GCF of 32 and 72 is the largest possible number that divides 32 and 72 exactly without any remainder. The factors of 32 and 72 are 1, 2, 4, 8, 16, 32 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 32 and 72 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 32 and 72 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 32 and 72?
Answer: GCF of 32 and 72 is 8.
Explanation:
The GCF of two non-zero integers, x(32) and y(72), is the greatest positive integer m(8) that divides both x(32) and y(72) without any remainder.
Methods to Find GCF of 32 and 72
The methods to find the GCF of 32 and 72 are explained below.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 32 and 72 by Listing Common Factors
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
There are 4 common factors of 32 and 72, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 32 and 72 is 8.
GCF of 32 and 72 by Long Division
GCF of 32 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 32 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (8).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (8) is the GCF of 32 and 72.
GCF of 32 and 72 by Prime Factorization
Prime factorization of 32 and 72 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 32 and 72 have common prime factors. Hence, the GCF of 32 and 72 is 2 × 2 × 2 = 8.
☛ Also Check:
- GCF of 14 and 15 = 1
- GCF of 92 and 23 = 23
- GCF of 25 and 45 = 5
- GCF of 7 and 56 = 7
- GCF of 9 and 30 = 3
- GCF of 24 and 36 = 12
- GCF of 39 and 6 = 3
GCF of 32 and 72 Examples
Example 1: For two numbers, GCF = 8 and LCM = 288. If one number is 72, find the other number.
Solution:
See AlsoCORRECT WAY TO CLIMB LADDERSGiven: GCF (y, 72) = 8 and LCM (y, 72) = 288
∵ GCF × LCM = 72 × (y)
⇒ y = (GCF × LCM)/72
⇒ y = (8 × 288)/72
⇒ y = 32
Therefore, the other number is 32.Example 2: The product of two numbers is 2304. If their GCF is 8, what is their LCM?
Solution:
Given: GCF = 8 and product of numbers = 2304
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2304/8
Therefore, the LCM is 288.Example 3: Find the GCF of 32 and 72, if their LCM is 288.
Solution:
∵ LCM × GCF = 32 × 72
⇒ GCF(32, 72) = (32 × 72)/288 = 8
Therefore, the greatest common factor of 32 and 72 is 8.
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FAQs on GCF of 32 and 72
What is the GCF of 32 and 72?
The GCF of 32 and 72 is 8. To calculate the greatest common factor (GCF) of 32 and 72, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 32 and 72, i.e., 8.
How to Find the GCF of 32 and 72 by Long Division Method?
To find the GCF of 32, 72 using long division method, 72 is divided by 32. The corresponding divisor (8) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 32, 72?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 32 and 72, i.e. GCF × LCM = 32 × 72.
How to Find the GCF of 32 and 72 by Prime Factorization?
To find the GCF of 32 and 72, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 32 and 72. Hence, GCF(32, 72) = 2 × 2 × 2 = 8
☛ What are Prime Numbers?
What are the Methods to Find GCF of 32 and 72?
There are three commonly used methods to find the GCF of 32 and 72.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
If the GCF of 72 and 32 is 8, Find its LCM.
GCF(72, 32) × LCM(72, 32) = 72 × 32
Since the GCF of 72 and 32 = 8
⇒ 8 × LCM(72, 32) = 2304
Therefore, LCM = 288
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