How to Find GCF of 340/749, 2100/9200?

GCF of 340/749, 2100/9200

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 340/749, 2100/9200 i.e 20/6890800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/749, 2100/9200.

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 340/749,2100/9200?

Given fractions are 340/749,2100/9200

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 340/749,2100/9200, numerators are 340,2100

Denominators are 749,9200

The GCF of 340,2100 is 20 .

LCM of 749,9200 is 6890800.

The greatest common factor of 340/749,2100/9200 = [GCF of 340,2100]/[LCM of 749,9200]= 20/6890800

Therefore, the GCF of 340/749,2100/9200 is 20/6890800.

Greatest Common Factor of 340,2100

To find the highest common factor of 340,2100, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100

The HCF of 340,2100 is 20.

Lets's calculate GCF of 340,2100

Greatest Common Factor (GCF) of 340,2100 By Common Division

2	340, 2100
2	170, 1050
5	85, 525
	17, 105

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 340,2100 By Matching Biggest Common Factor Method

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 2100

1,2,3,4,5,6,7,10,12,14,15,20,21,25,28,30,35,42,50,60,70,75,84,100,105,140,150,175,210,300,350,420,525,700,1050,2100

Greatest Common Factor

We found the factors 340,2100 . The biggest common factor number is the GCF number.
So the greatest common factor 340,2100 is 20.

Lets's calculate LCM of 749,9200

Lowest Common Multiple of 749,9200 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 6890800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/6890800

Therefore, the GCF of Fractions 340/749,2100/9200 is 20/6890800

Least Common Multiple of 749,9200 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 749,9200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(749,9200) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(749,9200) x common factors =1 x 1 = 1

LCM(749,9200) = ( 749 × 9200 ) / 1

LCM(749,9200) = 6890800 / 1

LCM(749,9200) = 6890800

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 340/749, 2100/9200

1. What is the HCF of 340,2100?

The HCF of 340,2100 is 20

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 340/749, 2100/9200?

Answer: GCF of Numerators as per given numbers 340/749, 2100/9200 is

GCF of Numerators i.e. for 340,2100 is 20

LCM of denominators i.e. for 749,9200 is 6890800.

Thus, GCF of Fractions is 20/6890800.Finally, GCF of Fractions for 340/749, 2100/9200 is 20/6890800.