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GCF of 105 and 90

GCF of 105 and 90 is the largest possible number that divides 105 and 90 exactly without any remainder. The factors of 105 and 90 are 1, 3, 5, 7, 15, 21, 35, 105 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 105 and 90 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 105 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 105 and 90?

Answer: GCF of 105 and 90 is 15.

Explanation:

The GCF of two non-zero integers, x(105) and y(90), is the greatest positive integer m(15) that divides both x(105) and y(90) without any remainder.

Methods to Find GCF of 105 and 90

The methods to find the GCF of 105 and 90 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 105 and 90 by Long Division

GCF of 105 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 105 (larger number) by 90 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (90) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 105 and 90.

GCF of 105 and 90 by Prime Factorization

Prime factorization of 105 and 90 is (3 × 5 × 7) and (2 × 3 × 3 × 5) respectively. As visible, 105 and 90 have common prime factors. Hence, the GCF of 105 and 90 is 3 × 5 = 15.

GCF of 105 and 90 by Listing Common Factors

Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 105 and 90, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 105 and 90 is 15.

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GCF of 105 and 90 Examples

Example 1: Find the GCF of 105 and 90, if their LCM is 630.

Solution:

∵ LCM × GCF = 105 × 90
⇒ GCF(105, 90) = (105 × 90)/630 = 15
Therefore, the greatest common factor of 105 and 90 is 15.
Example 2: The product of two numbers is 9450. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 9450
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 9450/15
Therefore, the LCM is 630.
Example 3: For two numbers, GCF = 15 and LCM = 630. If one number is 90, find the other number.

Solution:

Given: GCF (z, 90) = 15 and LCM (z, 90) = 630
∵ GCF × LCM = 90 × (z)
⇒ z = (GCF × LCM)/90
⇒ z = (15 × 630)/90
⇒ z = 105
Therefore, the other number is 105.

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FAQs on GCF of 105 and 90

What is the GCF of 105 and 90?

The GCF of 105 and 90 is 15. To calculate the GCF of 105 and 90, we need to factor each number (factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 105 and 90, i.e., 15.

If the GCF of 90 and 105 is 15, Find its LCM.

GCF(90, 105) × LCM(90, 105) = 90 × 105
Since the GCF of 90 and 105 = 15
⇒ 15 × LCM(90, 105) = 9450
Therefore, LCM = 630
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How to Find the GCF of 105 and 90 by Long Division Method?

To find the GCF of 105, 90 using long division method, 105 is divided by 90. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 105 and 90?

There are three commonly used methods to find the GCF of 105 and 90.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and GCF of 105, 90?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 105 and 90, i.e. GCF × LCM = 105 × 90.

How to Find the GCF of 105 and 90 by Prime Factorization?

To find the GCF of 105 and 90, we will find the prime factorization of the given numbers, i.e. 105 = 3 × 5 × 7; 90 = 2 × 3 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 105 and 90. Hence, GCF(105, 90) = 3 × 5 = 15
☛ What are Prime Numbers?

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