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GCF of 70 and 100

GCF of 70 and 100 is the largest possible number that divides 70 and 100 exactly without any remainder. The factors of 70 and 100 are 1, 2, 5, 7, 10, 14, 35, 70 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 70 and 100 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 70 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 70 and 100?

Answer: GCF of 70 and 100 is 10.

Explanation:

The GCF of two non-zero integers, x(70) and y(100), is the greatest positive integer m(10) that divides both x(70) and y(100) without any remainder.

Methods to Find GCF of 70 and 100

Let's look at the different methods for finding the GCF of 70 and 100.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 70 and 100 by Long Division

GCF of 70 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 70 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (70) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 70 and 100.

GCF of 70 and 100 by Prime Factorization

Prime factorization of 70 and 100 is (2 × 5 × 7) and (2 × 2 × 5 × 5) respectively. As visible, 70 and 100 have common prime factors. Hence, the GCF of 70 and 100 is 2 × 5 = 10.

GCF of 70 and 100 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 = 100 and Y = 70

GCF(100, 70) = GCF(70, 100 mod 70) = GCF(70, 30)
GCF(70, 30) = GCF(30, 70 mod 30) = GCF(30, 10)
GCF(30, 10) = GCF(10, 30 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 70 and 100 is 10.

☛ Also Check:

GCF of 70 and 100 Examples

Example 1: Find the GCF of 70 and 100, if their LCM is 700.

Solution:

∵ LCM × GCF = 70 × 100
⇒ GCF(70, 100) = (70 × 100)/700 = 10
Therefore, the greatest common factor of 70 and 100 is 10.
Example 2: The product of two numbers is 7000. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 7000
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 7000/10
Therefore, the LCM is 700.
Example 3: Find the greatest number that divides 70 and 100 exactly.

Solution:

The greatest number that divides 70 and 100 exactly is their greatest common factor, i.e. GCF of 70 and 100.
⇒ Factors of 70 and 100:
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 70 and 100 is 10.

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FAQs on GCF of 70 and 100

What is the GCF of 70 and 100?

The GCF of 70 and 100 is 10. To calculate the GCF (Greatest Common Factor) of 70 and 100, we need to factor each number (factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 70 and 100, i.e., 10.

What are the Methods to Find GCF of 70 and 100?

There are three commonly used methods to find the GCF of 70 and 100.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 100 and 70 is 10, Find its LCM.

GCF(100, 70) × LCM(100, 70) = 100 × 70
Since the GCF of 100 and 70 = 10
⇒ 10 × LCM(100, 70) = 7000
Therefore, LCM = 700
☛ Greatest Common Factor Calculator

How to Find the GCF of 70 and 100 by Prime Factorization?

To find the GCF of 70 and 100, we will find the prime factorization of the given numbers, i.e. 70 = 2 × 5 × 7; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 70 and 100. Hence, GCF(70, 100) = 2 × 5 = 10
☛ Prime Numbers

How to Find the GCF of 70 and 100 by Long Division Method?

To find the GCF of 70, 100 using long division method, 100 is divided by 70. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 70, 100?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 70 and 100, i.e. GCF × LCM = 70 × 100.

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