GCF of 27 and 63
GCF of 27 and 63 is the largest possible number that divides 27 and 63 exactly without any remainder. The factors of 27 and 63 are 1, 3, 9, 27 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 27 and 63 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 27 and 63 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 27 and 63?
Answer: GCF of 27 and 63 is 9.
Explanation:
The GCF of two non-zero integers, x(27) and y(63), is the greatest positive integer m(9) that divides both x(27) and y(63) without any remainder.
Methods to Find GCF of 27 and 63
Let's look at the different methods for finding the GCF of 27 and 63.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
GCF of 27 and 63 by Prime Factorization
Prime factorization of 27 and 63 is (3 × 3 × 3) and (3 × 3 × 7) respectively. As visible, 27 and 63 have common prime factors. Hence, the GCF of 27 and 63 is 3 × 3 = 9.
GCF of 27 and 63 by Listing Common Factors
- Factors of 27: 1, 3, 9, 27
- Factors of 63: 1, 3, 7, 9, 21, 63
There are 3 common factors of 27 and 63, that are 1, 3, and 9. Therefore, the greatest common factor of 27 and 63 is 9.
GCF of 27 and 63 by Long Division
GCF of 27 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 63 (larger number) by 27 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (9).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (9) is the GCF of 27 and 63.
☛ Also Check:
- GCF of 48 and 60 = 12
- GCF of 36 and 42 = 6
- GCF of 8 and 24 = 8
- GCF of 3 and 12 = 3
- GCF of 12 and 45 = 3
- GCF of 13 and 26 = 13
- GCF of 20 and 36 = 4
FAQs on GCF of 27 and 63
What is the GCF of 27 and 63?
The GCF of 27 and 63 is 9. To calculate the greatest common factor (GCF) of 27 and 63, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 27 and 63, i.e., 9.
How to Find the GCF of 27 and 63 by Long Division Method?
To find the GCF of 27, 63 using long division method, 63 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as GCF.
How to Find the GCF of 27 and 63 by Prime Factorization?
To find the GCF of 27 and 63, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 63 = 3 × 3 × 7.
⇒ Since 3, 3 are common terms in the prime factorization of 27 and 63. Hence, GCF(27, 63) = 3 × 3 = 9
☛ What is a Prime Number?
If the GCF of 63 and 27 is 9, Find its LCM.
GCF(63, 27) × LCM(63, 27) = 63 × 27
Since the GCF of 63 and 27 = 9
⇒ 9 × LCM(63, 27) = 1701
Therefore, LCM = 189
☛ GCF Calculator
What is the Relation Between LCM and GCF of 27, 63?
The following equation can be used to express the relation between LCM and GCF of 27 and 63, i.e. GCF × LCM = 27 × 63.
What are the Methods to Find GCF of 27 and 63?
There are three commonly used methods to find the GCF of 27 and 63.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division