How to Find GCF of 688/712, 3042/367?

GCF of 688/712, 3042/367

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 688/712, 3042/367 i.e 2/261304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/712, 3042/367.

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 688/712,3042/367?

Given fractions are 688/712,3042/367

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 688/712,3042/367, numerators are 688,3042

Denominators are 712,367

The GCF of 688,3042 is 2 .

LCM of 712,367 is 261304.

The greatest common factor of 688/712,3042/367 = [GCF of 688,3042]/[LCM of 712,367]= 2/261304

Therefore, the GCF of 688/712,3042/367 is 2/261304.

Greatest Common Factor of 688,3042

To find the highest common factor of 688,3042, we have to find the factors of both numbers and list the highest common factor.

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688

The factors of 3042 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 169, 234, 338, 507, 1014, 1521, 3042

The HCF of 688,3042 is 2.

Lets's calculate GCF of 688,3042

Greatest Common Factor (GCF) of 688,3042 By Common Division

2	688, 3042
	344, 1521

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

Greatest Common Factor of 688,3042 By Matching Biggest Common Factor Method

Now, list down the factors of 688

1,2,4,8,16,43,86,172,344,688

Now, list down the factors of 3042

1,2,3,6,9,13,18,26,39,78,117,169,234,338,507,1014,1521,3042

Greatest Common Factor

We found the factors 688,3042 . The biggest common factor number is the GCF number.
So the greatest common factor 688,3042 is 2.

Lets's calculate LCM of 712,367

Lowest Common Multiple of 712,367 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 261304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/261304

Therefore, the GCF of Fractions 688/712,3042/367 is 2/261304

Least Common Multiple of 712,367 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 712,367 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(712,367) = 1

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

GCF(712,367) x common factors =1 x 1 = 1

LCM(712,367) = ( 712 × 367 ) / 1

LCM(712,367) = 261304 / 1

LCM(712,367) = 261304

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FAQs on GCF of Fractions of 688/712, 3042/367

1. What is the HCF of 688,3042?

The HCF of 688,3042 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 688/712, 3042/367?

Answer: GCF of Numerators as per given numbers 688/712, 3042/367 is

GCF of Numerators i.e. for 688,3042 is 2

LCM of denominators i.e. for 712,367 is 261304.

Thus, GCF of Fractions is 2/261304.Finally, GCF of Fractions for 688/712, 3042/367 is 2/261304.