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

GCF of 45 and 70

GCF of 45 and 70 is the largest possible number that divides 45 and 70 exactly without any remainder. The factors of 45 and 70 are 1, 3, 5, 9, 15, 45 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 45 and 70 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 45 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 70?

Answer: GCF of 45 and 70 is 5.

Explanation:

The GCF of two non-zero integers, x(45) and y(70), is the greatest positive integer m(5) that divides both x(45) and y(70) without any remainder.

Methods to Find GCF of 45 and 70

Let's look at the different methods for finding the GCF of 45 and 70.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 45 and 70 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

There are 2 common factors of 45 and 70, that are 1 and 5. Therefore, the greatest common factor of 45 and 70 is 5.

GCF of 45 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 = 45

GCF(70, 45) = GCF(45, 70 mod 45) = GCF(45, 25)
GCF(45, 25) = GCF(25, 45 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 45 and 70 is 5.

GCF of 45 and 70 by Long Division

GCF of 45 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 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (25).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 45 and 70.

☛ Also Check:

GCF of 45 and 70 Examples

Example 1: Find the GCF of 45 and 70, if their LCM is 630.

Solution:

∵ LCM × GCF = 45 × 70
⇒ GCF(45, 70) = (45 × 70)/630 = 5
Therefore, the greatest common factor of 45 and 70 is 5.
Example 2: For two numbers, GCF = 5 and LCM = 630. If one number is 70, find the other number.

Solution:

Given: GCF (z, 70) = 5 and LCM (z, 70) = 630
∵ GCF × LCM = 70 × (z)
⇒ z = (GCF × LCM)/70
⇒ z = (5 × 630)/70
⇒ z = 45
Therefore, the other number is 45.
Example 3: The product of two numbers is 3150. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 3150
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3150/5
Therefore, the LCM is 630.

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 45 and 70

What is the GCF of 45 and 70?

The GCF of 45 and 70 is 5. To calculate the GCF (Greatest Common Factor) of 45 and 70, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides both 45 and 70, i.e., 5.

What are the Methods to Find GCF of 45 and 70?

There are three commonly used methods to find the GCF of 45 and 70.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 45, 70?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 45 and 70, i.e. GCF × LCM = 45 × 70.

How to Find the GCF of 45 and 70 by Prime Factorization?

To find the GCF of 45 and 70, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 70 = 2 × 5 × 7.
⇒ Since 5 is the only common prime factor of 45 and 70. Hence, GCF (45, 70) = 5.
☛ What is a Prime Number?

How to Find the GCF of 45 and 70 by Long Division Method?

To find the GCF of 45, 70 using long division method, 70 is divided by 45. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

If the GCF of 70 and 45 is 5, Find its LCM.

GCF(70, 45) × LCM(70, 45) = 70 × 45
Since the GCF of 70 and 45 = 5
⇒ 5 × LCM(70, 45) = 3150
Therefore, LCM = 630
☛ Greatest Common Factor Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum