How to Find GCF of 105/776, 300/848?

GCF of 105/776, 300/848

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 105/776, 300/848 i.e 15/82256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/776, 300/848.

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 105/776,300/848?

Given fractions are 105/776,300/848

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 105/776,300/848, numerators are 105,300

Denominators are 776,848

The GCF of 105,300 is 15 .

LCM of 776,848 is 82256.

The greatest common factor of 105/776,300/848 = [GCF of 105,300]/[LCM of 776,848]= 15/82256

Therefore, the GCF of 105/776,300/848 is 15/82256.

Greatest Common Factor of 105,300

To find the highest common factor of 105,300, we have to find the factors of both numbers and list the highest common factor.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The HCF of 105,300 is 15.

Lets's calculate GCF of 105,300

Greatest Common Factor (GCF) of 105,300 By Common Division

3	105, 300
5	35, 100
	7, 20

∴ So the GCF of the given numbers is 3 x 5 = 15

Greatest Common Factor of 105,300 By Matching Biggest Common Factor Method

Now, list down the factors of 105

1,3,5,7,15,21,35,105

Now, list down the factors of 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 105,300 . The biggest common factor number is the GCF number.
So the greatest common factor 105,300 is 15.

Lets's calculate LCM of 776,848

Lowest Common Multiple of 776,848 using Common Division

2	776, 848
2	388, 424
2	194, 212
	97, 106

∴ So the LCM of the given numbers is 2 x 2 x 2 x 97 x 106 = 82256

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/82256

Therefore, the GCF of Fractions 105/776,300/848 is 15/82256

Least Common Multiple of 776,848 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 776,848 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(776,848) = 8

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

GCF(776,848) x common factors =8 x 1 = 8

LCM(776,848) = ( 776 × 848 ) / 8

LCM(776,848) = 658048 / 8

LCM(776,848) = 82256

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FAQs on GCF of Fractions of 105/776, 300/848

1. What is the HCF of 105,300?

The HCF of 105,300 is 15

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 105/776, 300/848?

Answer: GCF of Numerators as per given numbers 105/776, 300/848 is

GCF of Numerators i.e. for 105,300 is 15

LCM of denominators i.e. for 776,848 is 82256.

Thus, GCF of Fractions is 15/82256.Finally, GCF of Fractions for 105/776, 300/848 is 15/82256.