How to Find GCF of 24/26, 340/14, 162/300?

GCF of 24/26, 340/14, 162/300

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 24/26, 340/14, 162/300 i.e 2/27300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 24/26, 340/14, 162/300.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 24/26,340/14,162/300?

Given fractions are 24/26,340/14,162/300

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 24/26,340/14,162/300, numerators are 24,340,162

Denominators are 26,14,300

The GCF of 24,340,162 is 2 .

LCM of 26,14,300 is 27300.

The greatest common factor of 24/26,340/14,162/300 = [GCF of 24,340,162]/[LCM of 26,14,300]= 2/27300

Therefore, the GCF of 24/26,340/14,162/300 is 2/27300.

Greatest Common Factor of 24,340,162

To find the highest common factor of 24,340,162, we have to find the factors of both numbers and list the highest common factor.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162

The HCF of 24,340,162 is 2.

Lets's calculate GCF of 24,340,162

Greatest Common Factor (GCF) of 24,340,162 By Common Division

2	24, 340, 162
	12, 170, 81

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 24,340,162 By Matching Biggest Common Factor Method

Now, list down the factors of 24

1,2,3,4,6,8,12,24

Now, list down the factors of 340

1,2,4,5,10,17,20,34,68,85,170,340

Now, list down the factors of 162

1,2,3,6,9,18,27,54,81,162

Greatest Common Factor

We found the factors 24,340,162 . The biggest common factor number is the GCF number.
So the greatest common factor 24,340,162 is 2.

Lets's calculate LCM of 26,14,300

Lowest Common Multiple of 26,14,300 using Common Division

2	26, 14, 300
	13, 7, 150

∴ So the LCM of the given numbers is 2 x 13 x 7 x 150 = 27300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27300

Therefore, the GCF of Fractions 24/26,340/14,162/300 is 2/27300

Least Common Multiple of 26,14,300 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 26,14,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(26,14,300) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(26,14,300) x common factors =2 x 2 = 4

LCM(26,14,300) = ( 26 × 14 × 300 ) / 4

LCM(26,14,300) = 109200 / 4

LCM(26,14,300) = 27300

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FAQs on GCF of Fractions of 24/26, 340/14, 162/300

1. What is the HCF of 24,340,162?

The HCF of 24,340,162 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 24/26, 340/14, 162/300?

Answer: GCF of Numerators as per given numbers 24/26, 340/14, 162/300 is

GCF of Numerators i.e. for 24,340,162 is 2

LCM of denominators i.e. for 26,14,300 is 27300.

Thus, GCF of Fractions is 2/27300.Finally, GCF of Fractions for 24/26, 340/14, 162/300 is 2/27300.