GCF of 698/78, 172/2031
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 698/78, 172/2031 i.e 2/52806 easily. The following is the detailed procedure to determine the greatest common factor of fractions 698/78, 172/2031.
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 698/78,172/2031?
Given fractions are 698/78,172/2031
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 698/78,172/2031, numerators are 698,172
Denominators are 78,2031
The GCF of 698,172 is 2 .
LCM of 78,2031 is 52806.
The greatest common factor of 698/78,172/2031 = [GCF of 698,172]/[LCM of 78,2031]= 2/52806
Therefore, the GCF of 698/78,172/2031 is 2/52806.
To find the highest common factor of 698,172, we have to find the factors of both numbers and list the highest common factor.
The factors of 698 are 1, 2, 349, 698
The factors of 172 are 1, 2, 4, 43, 86, 172
The HCF of 698,172 is 2.
Lets's calculate GCF of 698,172
| 2 | 698, 172 |
| 349, 86 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 698,172 By Matching Biggest Common Factor Method
Now, list down the factors of 698
:1,2,349,698
Now, list down the factors of 172
:1,2,4,43,86,172
Greatest Common Factor
We found the factors 698,172 . The biggest common factor number is the GCF number.
So the greatest common factor 698,172 is 2.
Lets's calculate LCM of 78,2031
| 3 | 78, 2031 |
| 26, 677 |
∴ So the LCM of the given numbers is 3 x 26 x 677 = 52806
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/52806
Therefore, the GCF of Fractions 698/78,172/2031 is 2/52806
Least Common Multiple of 78,2031 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 78,2031 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,2031) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(78,2031) x common factors =3 x 1 = 3
LCM(78,2031) = ( 78 × 2031 ) / 3
LCM(78,2031) = 158418 / 3
LCM(78,2031) = 52806
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FAQs on GCF of Fractions of 698/78, 172/2031
1. What is the HCF of 698,172?
The HCF of 698,172 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 698/78, 172/2031?
Answer: GCF of Numerators as per given numbers 698/78, 172/2031 is
GCF of Numerators i.e. for 698,172 is 2
LCM of denominators i.e. for 78,2031 is 52806.
Thus, GCF of Fractions is 2/52806.Finally, GCF of Fractions for 698/78, 172/2031 is 2/52806.