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GCF of 70 and 98

GCF of 70 and 98 is the largest possible number that divides 70 and 98 exactly without any remainder. The factors of 70 and 98 are 1, 2, 5, 7, 10, 14, 35, 70 and 1, 2, 7, 14, 49, 98 respectively. There are 3 commonly used methods to find the GCF of 70 and 98 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 70 and 98
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 70 and 98?

Answer: GCF of 70 and 98 is 14.

Explanation:

The GCF of two non-zero integers, x(70) and y(98), is the greatest positive integer m(14) that divides both x(70) and y(98) without any remainder.

Methods to Find GCF of 70 and 98

The methods to find the GCF of 70 and 98 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 70 and 98 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 = 98 and Y = 70

GCF(98, 70) = GCF(70, 98 mod 70) = GCF(70, 28)
GCF(70, 28) = GCF(28, 70 mod 28) = GCF(28, 14)
GCF(28, 14) = GCF(14, 28 mod 14) = GCF(14, 0)
GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 70 and 98 is 14.

GCF of 70 and 98 by Long Division

GCF of 70 and 98 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 98 (larger number) by 70 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (70) by the remainder (28).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (14) is the GCF of 70 and 98.

GCF of 70 and 98 by Prime Factorization

Prime factorization of 70 and 98 is (2 × 5 × 7) and (2 × 7 × 7) respectively. As visible, 70 and 98 have common prime factors. Hence, the GCF of 70 and 98 is 2 × 7 = 14.

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GCF of 70 and 98 Examples

Example 1: The product of two numbers is 6860. If their GCF is 14, what is their LCM?

Solution:

Given: GCF = 14 and product of numbers = 6860
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6860/14
Therefore, the LCM is 490.
Example 2: For two numbers, GCF = 14 and LCM = 490. If one number is 98, find the other number.

Solution:

Given: GCF (z, 98) = 14 and LCM (z, 98) = 490
∵ GCF × LCM = 98 × (z)
⇒ z = (GCF × LCM)/98
⇒ z = (14 × 490)/98
⇒ z = 70
Therefore, the other number is 70.
Example 3: Find the greatest number that divides 70 and 98 exactly.

Solution:

The greatest number that divides 70 and 98 exactly is their greatest common factor, i.e. GCF of 70 and 98.
⇒ Factors of 70 and 98:
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 98 = 1, 2, 7, 14, 49, 98
Therefore, the GCF of 70 and 98 is 14.

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FAQs on GCF of 70 and 98

What is the GCF of 70 and 98?

The GCF of 70 and 98 is 14. To calculate the greatest common factor of 70 and 98, we need to factor each number (factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70; factors of 98 = 1, 2, 7, 14, 49, 98) and choose the greatest factor that exactly divides both 70 and 98, i.e., 14.

How to Find the GCF of 70 and 98 by Long Division Method?

To find the GCF of 70, 98 using long division method, 98 is divided by 70. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

If the GCF of 98 and 70 is 14, Find its LCM.

GCF(98, 70) × LCM(98, 70) = 98 × 70
Since the GCF of 98 and 70 = 14
⇒ 14 × LCM(98, 70) = 6860
Therefore, LCM = 490
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What are the Methods to Find GCF of 70 and 98?

There are three commonly used methods to find the GCF of 70 and 98.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and GCF of 70, 98?

The following equation can be used to express the relation between LCM and GCF of 70 and 98, i.e. GCF × LCM = 70 × 98.

How to Find the GCF of 70 and 98 by Prime Factorization?

To find the GCF of 70 and 98, we will find the prime factorization of the given numbers, i.e. 70 = 2 × 5 × 7; 98 = 2 × 7 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 70 and 98. Hence, GCF(70, 98) = 2 × 7 = 14
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