How to Find GCF of 60/53, 748/66, 120/974?

GCF of 60/53, 748/66, 120/974

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 60/53, 748/66, 120/974 i.e 4/1703526 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/53, 748/66, 120/974.

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 60/53,748/66,120/974?

Given fractions are 60/53,748/66,120/974

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 60/53,748/66,120/974, numerators are 60,748,120

Denominators are 53,66,974

The GCF of 60,748,120 is 4 .

LCM of 53,66,974 is 1703526.

The greatest common factor of 60/53,748/66,120/974 = [GCF of 60,748,120]/[LCM of 53,66,974]= 4/1703526

Therefore, the GCF of 60/53,748/66,120/974 is 4/1703526.

Greatest Common Factor of 60,748,120

To find the highest common factor of 60,748,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The HCF of 60,748,120 is 4.

Lets's calculate GCF of 60,748,120

Greatest Common Factor (GCF) of 60,748,120 By Common Division

2	60, 748, 120
2	30, 374, 60
	15, 187, 30

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 60,748,120 By Matching Biggest Common Factor Method

Now, list down the factors of 60

1,2,3,4,5,6,10,12,15,20,30,60

Now, list down the factors of 748

1,2,4,11,17,22,34,44,68,187,374,748

Now, list down the factors of 120

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors 60,748,120 . The biggest common factor number is the GCF number.
So the greatest common factor 60,748,120 is 4.

Lets's calculate LCM of 53,66,974

Lowest Common Multiple of 53,66,974 using Common Division

2	53, 66, 974
	53, 33, 487

∴ So the LCM of the given numbers is 2 x 53 x 33 x 487 = 1703526

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1703526

Therefore, the GCF of Fractions 60/53,748/66,120/974 is 4/1703526

Least Common Multiple of 53,66,974 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 53,66,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(53,66,974) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(53,66,974) x common factors =1 x 2 = 2

LCM(53,66,974) = ( 53 × 66 × 974 ) / 2

LCM(53,66,974) = 3407052 / 2

LCM(53,66,974) = 1703526

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FAQs on GCF of Fractions of 60/53, 748/66, 120/974

1. What is the HCF of 60,748,120?

The HCF of 60,748,120 is 4

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 60/53, 748/66, 120/974?

Answer: GCF of Numerators as per given numbers 60/53, 748/66, 120/974 is

GCF of Numerators i.e. for 60,748,120 is 4

LCM of denominators i.e. for 53,66,974 is 1703526.

Thus, GCF of Fractions is 4/1703526.Finally, GCF of Fractions for 60/53, 748/66, 120/974 is 4/1703526.