A day full of math games & activities. Find one near you.

GCF of 14 and 70

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

1.	GCF of 14 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 70?

Answer: GCF of 14 and 70 is 14.

Explanation:

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

Methods to Find GCF of 14 and 70

Let's look at the different methods for finding the GCF of 14 and 70.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 14 and 70 by Long Division

GCF of 14 and 70 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 70 (larger number) by 14 (smaller number).
Step 2: Since the remainder = 0, the divisor (14) is the GCF of 14 and 70.

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

GCF of 14 and 70 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 = 70 and Y = 14

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

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

GCF of 14 and 70 by Listing Common Factors

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

There are 4 common factors of 14 and 70, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 14 and 70 is 14.

☛ Also Check:

GCF of 14 and 70 Examples

Example 1: Find the GCF of 14 and 70, if their LCM is 70.

Solution:

∵ LCM × GCF = 14 × 70
⇒ GCF(14, 70) = (14 × 70)/70 = 14
Therefore, the greatest common factor of 14 and 70 is 14.
Example 2: For two numbers, GCF = 14 and LCM = 70. If one number is 14, find the other number.

Solution:

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

Solution:

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

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 14 and 70

What is the GCF of 14 and 70?

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

How to Find the GCF of 14 and 70 by Long Division Method?

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

What is the Relation Between LCM and GCF of 14, 70?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 14 and 70, i.e. GCF × LCM = 14 × 70.

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

GCF(70, 14) × LCM(70, 14) = 70 × 14
Since the GCF of 70 and 14 = 14
⇒ 14 × LCM(70, 14) = 980
Therefore, LCM = 70
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 14 and 70?

There are three commonly used methods to find the GCF of 14 and 70.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 14 and 70 by Prime Factorization?

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

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum