GCF of 7750/314, 8988/3120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7750/314, 8988/3120 i.e 2/489840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7750/314, 8988/3120.
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 7750/314,8988/3120?
Given fractions are 7750/314,8988/3120
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 7750/314,8988/3120, numerators are 7750,8988
Denominators are 314,3120
The GCF of 7750,8988 is 2 .
LCM of 314,3120 is 489840.
The greatest common factor of 7750/314,8988/3120 = [GCF of 7750,8988]/[LCM of 314,3120]= 2/489840
Therefore, the GCF of 7750/314,8988/3120 is 2/489840.
To find the highest common factor of 7750,8988, we have to find the factors of both numbers and list the highest common factor.
The factors of 7750 are 1, 2, 5, 10, 25, 31, 50, 62, 125, 155, 250, 310, 775, 1550, 3875, 7750
The factors of 8988 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 107, 214, 321, 428, 642, 749, 1284, 1498, 2247, 2996, 4494, 8988
The HCF of 7750,8988 is 2.
Lets's calculate GCF of 7750,8988
| 2 | 7750, 8988 |
| 3875, 4494 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7750,8988 By Matching Biggest Common Factor Method
Now, list down the factors of 7750
:1,2,5,10,25,31,50,62,125,155,250,310,775,1550,3875,7750
Now, list down the factors of 8988
:1,2,3,4,6,7,12,14,21,28,42,84,107,214,321,428,642,749,1284,1498,2247,2996,4494,8988
Greatest Common Factor
We found the factors 7750,8988 . The biggest common factor number is the GCF number.
So the greatest common factor 7750,8988 is 2.
Lets's calculate LCM of 314,3120
| 2 | 314, 3120 |
| 157, 1560 |
∴ So the LCM of the given numbers is 2 x 157 x 1560 = 489840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/489840
Therefore, the GCF of Fractions 7750/314,8988/3120 is 2/489840
Least Common Multiple of 314,3120 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 314,3120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,3120) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(314,3120) x common factors =2 x 1 = 2
LCM(314,3120) = ( 314 × 3120 ) / 2
LCM(314,3120) = 979680 / 2
LCM(314,3120) = 489840
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FAQs on GCF of Fractions of 7750/314, 8988/3120
1. What is the HCF of 7750,8988?
The HCF of 7750,8988 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 7750/314, 8988/3120?
Answer: GCF of Numerators as per given numbers 7750/314, 8988/3120 is
GCF of Numerators i.e. for 7750,8988 is 2
LCM of denominators i.e. for 314,3120 is 489840.
Thus, GCF of Fractions is 2/489840.Finally, GCF of Fractions for 7750/314, 8988/3120 is 2/489840.