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GCF of 70 and 95

GCF of 70 and 95 is the largest possible number that divides 70 and 95 exactly without any remainder. The factors of 70 and 95 are 1, 2, 5, 7, 10, 14, 35, 70 and 1, 5, 19, 95 respectively. There are 3 commonly used methods to find the GCF of 70 and 95 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 70 and 95
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 70 and 95?

Answer: GCF of 70 and 95 is 5.

Explanation:

The GCF of two non-zero integers, x(70) and y(95), is the greatest positive integer m(5) that divides both x(70) and y(95) without any remainder.

Methods to Find GCF of 70 and 95

Let's look at the different methods for finding the GCF of 70 and 95.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 70 and 95 by Long Division

GCF of 70 and 95 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 95 (larger number) by 70 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (70) by the remainder (25).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 70 and 95.

GCF of 70 and 95 by Listing Common Factors

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 95: 1, 5, 19, 95

There are 2 common factors of 70 and 95, that are 1 and 5. Therefore, the greatest common factor of 70 and 95 is 5.

GCF of 70 and 95 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 = 95 and Y = 70

GCF(95, 70) = GCF(70, 95 mod 70) = GCF(70, 25)
GCF(70, 25) = GCF(25, 70 mod 25) = GCF(25, 20)
GCF(25, 20) = GCF(20, 25 mod 20) = GCF(20, 5)
GCF(20, 5) = GCF(5, 20 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 70 and 95 is 5.

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GCF of 70 and 95 Examples

Example 1: Find the greatest number that divides 70 and 95 exactly.

Solution:

The greatest number that divides 70 and 95 exactly is their greatest common factor, i.e. GCF of 70 and 95.
⇒ Factors of 70 and 95:
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 95 = 1, 5, 19, 95
Therefore, the GCF of 70 and 95 is 5.
Example 2: The product of two numbers is 6650. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 6650
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6650/5
Therefore, the LCM is 1330.
Example 3: For two numbers, GCF = 5 and LCM = 1330. If one number is 95, find the other number.

Solution:

Given: GCF (x, 95) = 5 and LCM (x, 95) = 1330
∵ GCF × LCM = 95 × (x)
⇒ x = (GCF × LCM)/95
⇒ x = (5 × 1330)/95
⇒ x = 70
Therefore, the other number is 70.

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FAQs on GCF of 70 and 95

What is the GCF of 70 and 95?

The GCF of 70 and 95 is 5. To calculate the greatest common factor (GCF) of 70 and 95, we need to factor each number (factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70; factors of 95 = 1, 5, 19, 95) and choose the greatest factor that exactly divides both 70 and 95, i.e., 5.

If the GCF of 95 and 70 is 5, Find its LCM.

GCF(95, 70) × LCM(95, 70) = 95 × 70
Since the GCF of 95 and 70 = 5
⇒ 5 × LCM(95, 70) = 6650
Therefore, LCM = 1330
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What is the Relation Between LCM and GCF of 70, 95?

The following equation can be used to express the relation between LCM and GCF of 70 and 95, i.e. GCF × LCM = 70 × 95.

How to Find the GCF of 70 and 95 by Long Division Method?

To find the GCF of 70, 95 using long division method, 95 is divided by 70. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 70 and 95?

There are three commonly used methods to find the GCF of 70 and 95.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 70 and 95 by Prime Factorization?

To find the GCF of 70 and 95, we will find the prime factorization of the given numbers, i.e. 70 = 2 × 5 × 7; 95 = 5 × 19.
⇒ Since 5 is the only common prime factor of 70 and 95. Hence, GCF (70, 95) = 5.
☛ What are Prime Numbers?

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