GCF of 99/67, 972/74, 741/278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 99/67, 972/74, 741/278 i.e 3/689162 easily. The following is the detailed procedure to determine the greatest common factor of fractions 99/67, 972/74, 741/278.
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 99/67,972/74,741/278?
Given fractions are 99/67,972/74,741/278
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 99/67,972/74,741/278, numerators are 99,972,741
Denominators are 67,74,278
The GCF of 99,972,741 is 3 .
LCM of 67,74,278 is 689162.
The greatest common factor of 99/67,972/74,741/278 = [GCF of 99,972,741]/[LCM of 67,74,278]= 3/689162
Therefore, the GCF of 99/67,972/74,741/278 is 3/689162.
To find the highest common factor of 99,972,741, we have to find the factors of both numbers and list the highest common factor.
The factors of 99 are 1, 3, 9, 11, 33, 99
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741
The HCF of 99,972,741 is 3.
Lets's calculate GCF of 99,972,741
| 3 | 99, 972, 741 |
| 33, 324, 247 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 99,972,741 By Matching Biggest Common Factor Method
Now, list down the factors of 99
:1,3,9,11,33,99
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 741
:1,3,13,19,39,57,247,741
Greatest Common Factor
We found the factors 99,972,741 . The biggest common factor number is the GCF number.
So the greatest common factor 99,972,741 is 3.
Lets's calculate LCM of 67,74,278
| 2 | 67, 74, 278 |
| 67, 37, 139 |
∴ So the LCM of the given numbers is 2 x 67 x 37 x 139 = 689162
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/689162
Therefore, the GCF of Fractions 99/67,972/74,741/278 is 3/689162
Least Common Multiple of 67,74,278 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 67,74,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,74,278) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(67,74,278) x common factors =1 x 2 = 2
LCM(67,74,278) = ( 67 × 74 × 278 ) / 2
LCM(67,74,278) = 1378324 / 2
LCM(67,74,278) = 689162
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FAQs on GCF of Fractions of 99/67, 972/74, 741/278
1. What is the HCF of 99,972,741?
The HCF of 99,972,741 is 3
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 99/67, 972/74, 741/278?
Answer: GCF of Numerators as per given numbers 99/67, 972/74, 741/278 is
GCF of Numerators i.e. for 99,972,741 is 3
LCM of denominators i.e. for 67,74,278 is 689162.
Thus, GCF of Fractions is 3/689162.Finally, GCF of Fractions for 99/67, 972/74, 741/278 is 3/689162.