GCF of 12/724, 76/877, 698/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 12/724, 76/877, 698/728 i.e 2/115560536 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/724, 76/877, 698/728.
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 12/724,76/877,698/728?
Given fractions are 12/724,76/877,698/728
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 12/724,76/877,698/728, numerators are 12,76,698
Denominators are 724,877,728
The GCF of 12,76,698 is 2 .
LCM of 724,877,728 is 115560536.
The greatest common factor of 12/724,76/877,698/728 = [GCF of 12,76,698]/[LCM of 724,877,728]= 2/115560536
Therefore, the GCF of 12/724,76/877,698/728 is 2/115560536.
To find the highest common factor of 12,76,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 698 are 1, 2, 349, 698
The HCF of 12,76,698 is 2.
Lets's calculate GCF of 12,76,698
| 2 | 12, 76, 698 |
| 6, 38, 349 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 12,76,698 By Matching Biggest Common Factor Method
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 12,76,698 . The biggest common factor number is the GCF number.
So the greatest common factor 12,76,698 is 2.
Lets's calculate LCM of 724,877,728
| 2 | 724, 877, 728 |
| 2 | 362, 877, 364 |
| 181, 877, 182 |
∴ So the LCM of the given numbers is 2 x 2 x 181 x 877 x 182 = 115560536
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/115560536
Therefore, the GCF of Fractions 12/724,76/877,698/728 is 2/115560536
Least Common Multiple of 724,877,728 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 724,877,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,877,728) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(724,877,728) x common factors =1 x 4 = 4
LCM(724,877,728) = ( 724 × 877 × 728 ) / 4
LCM(724,877,728) = 462242144 / 4
LCM(724,877,728) = 115560536
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FAQs on GCF of Fractions of 12/724, 76/877, 698/728
1. What is the HCF of 12,76,698?
The HCF of 12,76,698 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 12/724, 76/877, 698/728?
Answer: GCF of Numerators as per given numbers 12/724, 76/877, 698/728 is
GCF of Numerators i.e. for 12,76,698 is 2
LCM of denominators i.e. for 724,877,728 is 115560536.
Thus, GCF of Fractions is 2/115560536.Finally, GCF of Fractions for 12/724, 76/877, 698/728 is 2/115560536.