GCF of 34/42, 683/54, 980/917
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/42, 683/54, 980/917 i.e 1/49518 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/42, 683/54, 980/917.
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 34/42,683/54,980/917?
Given fractions are 34/42,683/54,980/917
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 34/42,683/54,980/917, numerators are 34,683,980
Denominators are 42,54,917
The GCF of 34,683,980 is 1 .
LCM of 42,54,917 is 49518.
The greatest common factor of 34/42,683/54,980/917 = [GCF of 34,683,980]/[LCM of 42,54,917]= 1/49518
Therefore, the GCF of 34/42,683/54,980/917 is 1/49518.
To find the highest common factor of 34,683,980, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 683 are 1, 683
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The HCF of 34,683,980 is 1.
Lets's calculate GCF of 34,683,980
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,683,980 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 683
:1,683
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Greatest Common Factor
We found the factors 34,683,980 . The biggest common factor number is the GCF number.
So the greatest common factor 34,683,980 is 1.
Lets's calculate LCM of 42,54,917
| 2 | 42, 54, 917 |
| 3 | 21, 27, 917 |
| 7 | 7, 9, 917 |
| 1, 9, 131 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1 x 9 x 131 = 49518
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/49518
Therefore, the GCF of Fractions 34/42,683/54,980/917 is 1/49518
Least Common Multiple of 42,54,917 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 42,54,917 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,54,917) = 1
common factors(in case of two or more numbers have common factors) = 42
GCF(42,54,917) x common factors =1 x 42 = 42
LCM(42,54,917) = ( 42 × 54 × 917 ) / 42
LCM(42,54,917) = 2079756 / 42
LCM(42,54,917) = 49518
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FAQs on GCF of Fractions of 34/42, 683/54, 980/917
1. What is the HCF of 34,683,980?
The HCF of 34,683,980 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 34/42, 683/54, 980/917?
Answer: GCF of Numerators as per given numbers 34/42, 683/54, 980/917 is
GCF of Numerators i.e. for 34,683,980 is 1
LCM of denominators i.e. for 42,54,917 is 49518.
Thus, GCF of Fractions is 1/49518.Finally, GCF of Fractions for 34/42, 683/54, 980/917 is 1/49518.