How to Find GCF of 825/196, 889/688?

GCF of 825/196, 889/688

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 825/196, 889/688 i.e 1/33712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/196, 889/688.

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 825/196,889/688?

Given fractions are 825/196,889/688

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 825/196,889/688, numerators are 825,889

Denominators are 196,688

The GCF of 825,889 is 1 .

LCM of 196,688 is 33712.

The greatest common factor of 825/196,889/688 = [GCF of 825,889]/[LCM of 196,688]= 1/33712

Therefore, the GCF of 825/196,889/688 is 1/33712.

Greatest Common Factor of 825,889

To find the highest common factor of 825,889, we have to find the factors of both numbers and list the highest common factor.

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

The factors of 889 are 1, 7, 127, 889

The HCF of 825,889 is 1.

Lets's calculate GCF of 825,889

Greatest Common Factor (GCF) of 825,889 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 825,889 By Matching Biggest Common Factor Method

Now, list down the factors of 825

1,3,5,11,15,25,33,55,75,165,275,825

Now, list down the factors of 889

1,7,127,889

Greatest Common Factor

We found the factors 825,889 . The biggest common factor number is the GCF number.
So the greatest common factor 825,889 is 1.

Lets's calculate LCM of 196,688

Lowest Common Multiple of 196,688 using Common Division

2	196, 688
2	98, 344
	49, 172

∴ So the LCM of the given numbers is 2 x 2 x 49 x 172 = 33712

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33712

Therefore, the GCF of Fractions 825/196,889/688 is 1/33712

Least Common Multiple of 196,688 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 196,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(196,688) = 4

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

GCF(196,688) x common factors =4 x 1 = 4

LCM(196,688) = ( 196 × 688 ) / 4

LCM(196,688) = 134848 / 4

LCM(196,688) = 33712

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FAQs on GCF of Fractions of 825/196, 889/688

1. What is the HCF of 825,889?

The HCF of 825,889 is 1

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 825/196, 889/688?

Answer: GCF of Numerators as per given numbers 825/196, 889/688 is

GCF of Numerators i.e. for 825,889 is 1

LCM of denominators i.e. for 196,688 is 33712.

Thus, GCF of Fractions is 1/33712.Finally, GCF of Fractions for 825/196, 889/688 is 1/33712.