GCF of 35 and 63
GCF of 35 and 63 is the largest possible number that divides 35 and 63 exactly without any remainder. The factors of 35 and 63 are 1, 5, 7, 35 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 35 and 63 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 35 and 63 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 35 and 63?
Answer: GCF of 35 and 63 is 7.
Explanation:
The GCF of two non-zero integers, x(35) and y(63), is the greatest positive integer m(7) that divides both x(35) and y(63) without any remainder.
Methods to Find GCF of 35 and 63
Let's look at the different methods for finding the GCF of 35 and 63.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
GCF of 35 and 63 by Listing Common Factors
- Factors of 35: 1, 5, 7, 35
- Factors of 63: 1, 3, 7, 9, 21, 63
There are 2 common factors of 35 and 63, that are 1 and 7. Therefore, the greatest common factor of 35 and 63 is 7.
GCF of 35 and 63 by Prime Factorization
Prime factorization of 35 and 63 is (5 × 7) and (3 × 3 × 7) respectively. As visible, 35 and 63 have only one common prime factor i.e. 7. Hence, the GCF of 35 and 63 is 7.
GCF of 35 and 63 by Long Division
GCF of 35 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 35 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (28).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the GCF of 35 and 63.
☛ Also Check:
- GCF of 52 and 78 = 26
- GCF of 81 and 48 = 3
- GCF of 8 and 36 = 4
- GCF of 68 and 34 = 34
- GCF of 30 and 48 = 6
- GCF of 50 and 72 = 2
- GCF of 40 and 48 = 8
FAQs on GCF of 35 and 63
What is the GCF of 35 and 63?
The GCF of 35 and 63 is 7. To calculate the greatest common factor (GCF) of 35 and 63, we need to factor each number (factors of 35 = 1, 5, 7, 35; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 35 and 63, i.e., 7.
How to Find the GCF of 35 and 63 by Long Division Method?
To find the GCF of 35, 63 using long division method, 63 is divided by 35. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 35, 63?
The following equation can be used to express the relation between LCM and GCF of 35 and 63, i.e. GCF × LCM = 35 × 63.
What are the Methods to Find GCF of 35 and 63?
There are three commonly used methods to find the GCF of 35 and 63.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
How to Find the GCF of 35 and 63 by Prime Factorization?
To find the GCF of 35 and 63, we will find the prime factorization of the given numbers, i.e. 35 = 5 × 7; 63 = 3 × 3 × 7.
⇒ Since 7 is the only common prime factor of 35 and 63. Hence, GCF (35, 63) = 7.
☛ Prime Numbers
If the GCF of 63 and 35 is 7, Find its LCM.
GCF(63, 35) × LCM(63, 35) = 63 × 35
Since the GCF of 63 and 35 = 7
⇒ 7 × LCM(63, 35) = 2205
Therefore, LCM = 315
☛ Greatest Common Factor Calculator