GCF of 3/82, 12/17, 61/506, 274/520
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/82, 12/17, 61/506, 274/520 i.e 1/91697320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/82, 12/17, 61/506, 274/520.
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 3/82,12/17,61/506,274/520?
Given fractions are 3/82,12/17,61/506,274/520
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 3/82,12/17,61/506,274/520, numerators are 3,12,61,274
Denominators are 82,17,506,520
The GCF of 3,12,61,274 is 1 .
LCM of 82,17,506,520 is 91697320.
The greatest common factor of 3/82,12/17,61/506,274/520 = [GCF of 3,12,61,274]/[LCM of 82,17,506,520]= 1/91697320
Therefore, the GCF of 3/82,12/17,61/506,274/520 is 1/91697320.
To find the highest common factor of 3,12,61,274, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 61 are 1, 61
The factors of 274 are 1, 2, 137, 274
The HCF of 3,12,61,274 is 1.
Lets's calculate GCF of 3,12,61,274
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,12,61,274 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 61
:1,61
Now, list down the factors of 274
:1,2,137,274
Greatest Common Factor
We found the factors 3,12,61,274 . The biggest common factor number is the GCF number.
So the greatest common factor 3,12,61,274 is 1.
Lets's calculate LCM of 82,17,506,520
| 2 | 82, 17, 506, 520 |
| 41, 17, 253, 260 |
∴ So the LCM of the given numbers is 2 x 41 x 17 x 253 x 260 = 91697320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/91697320
Therefore, the GCF of Fractions 3/82,12/17,61/506,274/520 is 1/91697320
Least Common Multiple of 82,17,506,520 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 82,17,506,520 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,17,506,520) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(82,17,506,520) x common factors =1 x 4 = 4
LCM(82,17,506,520) = ( 82 × 17 × 506 × 520 ) / 4
LCM(82,17,506,520) = 366789280 / 4
LCM(82,17,506,520) = 91697320
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3/82, 12/17, 61/506, 274/520
1. What is the HCF of 3,12,61,274?
The HCF of 3,12,61,274 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 3/82, 12/17, 61/506, 274/520?
Answer: GCF of Numerators as per given numbers 3/82, 12/17, 61/506, 274/520 is
GCF of Numerators i.e. for 3,12,61,274 is 1
LCM of denominators i.e. for 82,17,506,520 is 91697320.
Thus, GCF of Fractions is 1/91697320.Finally, GCF of Fractions for 3/82, 12/17, 61/506, 274/520 is 1/91697320.