How to Find GCF of 1882/780, 7568/1300?

GCF of 1882/780, 7568/1300

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 1882/780, 7568/1300 i.e 2/3900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1882/780, 7568/1300.

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 1882/780,7568/1300?

Given fractions are 1882/780,7568/1300

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 1882/780,7568/1300, numerators are 1882,7568

Denominators are 780,1300

The GCF of 1882,7568 is 2 .

LCM of 780,1300 is 3900.

The greatest common factor of 1882/780,7568/1300 = [GCF of 1882,7568]/[LCM of 780,1300]= 2/3900

Therefore, the GCF of 1882/780,7568/1300 is 2/3900.

Greatest Common Factor of 1882,7568

To find the highest common factor of 1882,7568, we have to find the factors of both numbers and list the highest common factor.

The factors of 1882 are 1, 2, 941, 1882

The factors of 7568 are 1, 2, 4, 8, 11, 16, 22, 43, 44, 86, 88, 172, 176, 344, 473, 688, 946, 1892, 3784, 7568

The HCF of 1882,7568 is 2.

Lets's calculate GCF of 1882,7568

Greatest Common Factor (GCF) of 1882,7568 By Common Division

2	1882, 7568
	941, 3784

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

Greatest Common Factor of 1882,7568 By Matching Biggest Common Factor Method

Now, list down the factors of 1882

1,2,941,1882

Now, list down the factors of 7568

1,2,4,8,11,16,22,43,44,86,88,172,176,344,473,688,946,1892,3784,7568

Greatest Common Factor

We found the factors 1882,7568 . The biggest common factor number is the GCF number.
So the greatest common factor 1882,7568 is 2.

Lets's calculate LCM of 780,1300

Lowest Common Multiple of 780,1300 using Common Division

2	780, 1300
2	390, 650
5	195, 325
13	39, 65
	3, 5

∴ So the LCM of the given numbers is 2 x 2 x 5 x 13 x 3 x 5 = 3900

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3900

Therefore, the GCF of Fractions 1882/780,7568/1300 is 2/3900

Least Common Multiple of 780,1300 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 780,1300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(780,1300) = 260

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

GCF(780,1300) x common factors =260 x 1 = 260

LCM(780,1300) = ( 780 × 1300 ) / 260

LCM(780,1300) = 1014000 / 260

LCM(780,1300) = 3900

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FAQs on GCF of Fractions of 1882/780, 7568/1300

1. What is the HCF of 1882,7568?

The HCF of 1882,7568 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 1882/780, 7568/1300?

Answer: GCF of Numerators as per given numbers 1882/780, 7568/1300 is

GCF of Numerators i.e. for 1882,7568 is 2

LCM of denominators i.e. for 780,1300 is 3900.

Thus, GCF of Fractions is 2/3900.Finally, GCF of Fractions for 1882/780, 7568/1300 is 2/3900.