GCF of 984/31, 784/265
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 984/31, 784/265 i.e 8/8215 easily. The following is the detailed procedure to determine the greatest common factor of fractions 984/31, 784/265.
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 984/31,784/265?
Given fractions are 984/31,784/265
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 984/31,784/265, numerators are 984,784
Denominators are 31,265
The GCF of 984,784 is 8 .
LCM of 31,265 is 8215.
The greatest common factor of 984/31,784/265 = [GCF of 984,784]/[LCM of 31,265]= 8/8215
Therefore, the GCF of 984/31,784/265 is 8/8215.
To find the highest common factor of 984,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 984,784 is 8.
Lets's calculate GCF of 984,784
| 2 | 984, 784 |
| 2 | 492, 392 |
| 2 | 246, 196 |
| 123, 98 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 984,784 By Matching Biggest Common Factor Method
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 984,784 . The biggest common factor number is the GCF number.
So the greatest common factor 984,784 is 8.
Lets's calculate LCM of 31,265
Given numbers has no common factors except 1. So, there LCM is their product i.e 8215
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/8215
Therefore, the GCF of Fractions 984/31,784/265 is 8/8215
Least Common Multiple of 31,265 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 31,265 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,265) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,265) x common factors =1 x 1 = 1
LCM(31,265) = ( 31 × 265 ) / 1
LCM(31,265) = 8215 / 1
LCM(31,265) = 8215
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FAQs on GCF of Fractions of 984/31, 784/265
1. What is the HCF of 984,784?
The HCF of 984,784 is 8
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 984/31, 784/265?
Answer: GCF of Numerators as per given numbers 984/31, 784/265 is
GCF of Numerators i.e. for 984,784 is 8
LCM of denominators i.e. for 31,265 is 8215.
Thus, GCF of Fractions is 8/8215.Finally, GCF of Fractions for 984/31, 784/265 is 8/8215.