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GCF of 35 and 45

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

1.	GCF of 35 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 35 and 45?

Answer: GCF of 35 and 45 is 5.

Explanation:

The GCF of two non-zero integers, x(35) and y(45), is the greatest positive integer m(5) that divides both x(35) and y(45) without any remainder.

Methods to Find GCF of 35 and 45

The methods to find the GCF of 35 and 45 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 35 and 45 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 = 45 and Y = 35

GCF(45, 35) = GCF(35, 45 mod 35) = GCF(35, 10)
GCF(35, 10) = GCF(10, 35 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 35 and 45 is 5.

GCF of 35 and 45 by Long Division

GCF of 35 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 35 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (35) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 35 and 45.

GCF of 35 and 45 by Listing Common Factors

Factors of 35: 1, 5, 7, 35
Factors of 45: 1, 3, 5, 9, 15, 45

There are 2 common factors of 35 and 45, that are 1 and 5. Therefore, the greatest common factor of 35 and 45 is 5.

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GCF of 35 and 45 Examples

Example 1: Find the GCF of 35 and 45, if their LCM is 315.

Solution:

∵ LCM × GCF = 35 × 45
⇒ GCF(35, 45) = (35 × 45)/315 = 5
Therefore, the greatest common factor of 35 and 45 is 5.
Example 2: The product of two numbers is 1575. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 1575
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1575/5
Therefore, the LCM is 315.
Example 3: Find the greatest number that divides 35 and 45 exactly.

Solution:

The greatest number that divides 35 and 45 exactly is their greatest common factor, i.e. GCF of 35 and 45.
⇒ Factors of 35 and 45:
- Factors of 35 = 1, 5, 7, 35
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 35 and 45 is 5.

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FAQs on GCF of 35 and 45

What is the GCF of 35 and 45?

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

How to Find the GCF of 35 and 45 by Long Division Method?

To find the GCF of 35, 45 using long division method, 45 is divided by 35. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 35 and 45?

There are three commonly used methods to find the GCF of 35 and 45.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 45 and 35 is 5, Find its LCM.

GCF(45, 35) × LCM(45, 35) = 45 × 35
Since the GCF of 45 and 35 = 5
⇒ 5 × LCM(45, 35) = 1575
Therefore, LCM = 315
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What is the Relation Between LCM and GCF of 35, 45?

The following equation can be used to express the relation between Least Common Multiple and GCF of 35 and 45, i.e. GCF × LCM = 35 × 45.

How to Find the GCF of 35 and 45 by Prime Factorization?

To find the GCF of 35 and 45, we will find the prime factorization of the given numbers, i.e. 35 = 5 × 7; 45 = 3 × 3 × 5.
⇒ Since 5 is the only common prime factor of 35 and 45. Hence, GCF (35, 45) = 5.
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