How to Find GCF of 74/308, 14/752, 499/745?

GCF of 74/308, 14/752, 499/745

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 74/308, 14/752, 499/745 i.e 1/43138480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/308, 14/752, 499/745.

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 74/308,14/752,499/745?

Given fractions are 74/308,14/752,499/745

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 74/308,14/752,499/745, numerators are 74,14,499

Denominators are 308,752,745

The GCF of 74,14,499 is 1 .

LCM of 308,752,745 is 43138480.

The greatest common factor of 74/308,14/752,499/745 = [GCF of 74,14,499]/[LCM of 308,752,745]= 1/43138480

Therefore, the GCF of 74/308,14/752,499/745 is 1/43138480.

Greatest Common Factor of 74,14,499

To find the highest common factor of 74,14,499, we have to find the factors of both numbers and list the highest common factor.

The factors of 74 are 1, 2, 37, 74

The factors of 14 are 1, 2, 7, 14

The factors of 499 are 1, 499

The HCF of 74,14,499 is 1.

Lets's calculate GCF of 74,14,499

Greatest Common Factor (GCF) of 74,14,499 By Common Division

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

Greatest Common Factor of 74,14,499 By Matching Biggest Common Factor Method

Now, list down the factors of 74

1,2,37,74

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 499

1,499

Greatest Common Factor

We found the factors 74,14,499 . The biggest common factor number is the GCF number.
So the greatest common factor 74,14,499 is 1.

Lets's calculate LCM of 308,752,745

Lowest Common Multiple of 308,752,745 using Common Division

2	308, 752, 745
2	154, 376, 745
	77, 188, 745

∴ So the LCM of the given numbers is 2 x 2 x 77 x 188 x 745 = 43138480

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43138480

Therefore, the GCF of Fractions 74/308,14/752,499/745 is 1/43138480

Least Common Multiple of 308,752,745 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 308,752,745 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(308,752,745) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(308,752,745) x common factors =1 x 4 = 4

LCM(308,752,745) = ( 308 × 752 × 745 ) / 4

LCM(308,752,745) = 172553920 / 4

LCM(308,752,745) = 43138480

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FAQs on GCF of Fractions of 74/308, 14/752, 499/745

1. What is the HCF of 74,14,499?

The HCF of 74,14,499 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 74/308, 14/752, 499/745?

Answer: GCF of Numerators as per given numbers 74/308, 14/752, 499/745 is

GCF of Numerators i.e. for 74,14,499 is 1

LCM of denominators i.e. for 308,752,745 is 43138480.

Thus, GCF of Fractions is 1/43138480.Finally, GCF of Fractions for 74/308, 14/752, 499/745 is 1/43138480.