GCF of 35 and 50 is the largest possible number that divides 35 and 50 exactly without any remainder. The factors of 35 and 50 are 1, 5, 7, 35 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 35 and 50 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 35 and 50 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 35 and 50?
Answer: GCF of 35 and 50 is 5.
Explanation:
The GCF of two non-zero integers, x(35) and y(50), is the greatest positive integer m(5) that divides both x(35) and y(50) without any remainder.
Methods to Find GCF of 35 and 50
The methods to find the GCF of 35 and 50 are explained below.
- Using Euclid's Algorithm
- Long Division Method
- Prime Factorization Method
GCF of 35 and 50 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 50 and Y = 35
- GCF(50, 35) = GCF(35, 50 mod 35) = GCF(35, 15)
- GCF(35, 15) = GCF(15, 35 mod 15) = GCF(15, 5)
- GCF(15, 5) = GCF(5, 15 mod 5) = GCF(5, 0)
- GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 35 and 50 is 5.
GCF of 35 and 50 by Long Division
GCF of 35 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 50 (larger number) by 35 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (15).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (5) is the GCF of 35 and 50.
GCF of 35 and 50 by Prime Factorization
Prime factorization of 35 and 50 is (5 × 7) and (2 × 5 × 5) respectively. As visible, 35 and 50 have only one common prime factor i.e. 5. Hence, the GCF of 35 and 50 is 5.
☛ Also Check:
- GCF of 64 and 32 = 32
- GCF of 18 and 27 = 9
- GCF of 56 and 70 = 14
- GCF of 24 and 28 = 4
- GCF of 24 and 64 = 8
- GCF of 75, 8 and 21 = 1
- GCF of 20 and 35 = 5
GCF of 35 and 50 Examples
Example 1: The product of two numbers is 1750. If their GCF is 5, what is their LCM?
Solution:
Given: GCF = 5 and product of numbers = 1750
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1750/5
Therefore, the LCM is 350.Example 2: Find the GCF of 35 and 50, if their LCM is 350.
Solution:
∵ LCM × GCF = 35 × 50
⇒ GCF(35, 50) = (35 × 50)/350 = 5
Therefore, the greatest common factor of 35 and 50 is 5.Example 3: Find the greatest number that divides 35 and 50 exactly.
Solution:
The greatest number that divides 35 and 50 exactly is their greatest common factor, i.e. GCF of 35 and 50.
⇒ Factors of 35 and 50:- Factors of 35 = 1, 5, 7, 35
- Factors of 50 = 1, 2, 5, 10, 25, 50
Therefore, the GCF of 35 and 50 is 5.
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FAQs on GCF of 35 and 50
What is the GCF of 35 and 50?
The GCF of 35 and 50 is 5. To calculate the GCF of 35 and 50, we need to factor each number (factors of 35 = 1, 5, 7, 35; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 35 and 50, i.e., 5.
What is the Relation Between LCM and GCF of 35, 50?
The following equation can be used to express the relation between Least Common Multiple and GCF of 35 and 50, i.e. GCF × LCM = 35 × 50.
What are the Methods to Find GCF of 35 and 50?
There are three commonly used methods to find the GCF of 35 and 50.
- By Listing Common Factors
- By Prime Factorization
- By Long Division
How to Find the GCF of 35 and 50 by Prime Factorization?
To find the GCF of 35 and 50, we will find the prime factorization of the given numbers, i.e. 35 = 5 × 7; 50 = 2 × 5 × 5.
⇒ Since 5 is the only common prime factor of 35 and 50. Hence, GCF (35, 50) = 5.
☛ What is a Prime Number?
How to Find the GCF of 35 and 50 by Long Division Method?
To find the GCF of 35, 50 using long division method, 50 is divided by 35. The corresponding divisor (5) when remainder equals 0 is taken as GCF.
If the GCF of 50 and 35 is 5, Find its LCM.
GCF(50, 35) × LCM(50, 35) = 50 × 35
Since the GCF of 50 and 35 = 5
⇒ 5 × LCM(50, 35) = 1750
Therefore, LCM = 350
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