GCF of 418/252, 7980/210
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 418/252, 7980/210 i.e 38/1260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 418/252, 7980/210.
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 418/252,7980/210?
Given fractions are 418/252,7980/210
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 418/252,7980/210, numerators are 418,7980
Denominators are 252,210
The GCF of 418,7980 is 38 .
LCM of 252,210 is 1260.
The greatest common factor of 418/252,7980/210 = [GCF of 418,7980]/[LCM of 252,210]= 38/1260
Therefore, the GCF of 418/252,7980/210 is 38/1260.
To find the highest common factor of 418,7980, we have to find the factors of both numbers and list the highest common factor.
The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418
The factors of 7980 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 28, 30, 35, 38, 42, 57, 60, 70, 76, 84, 95, 105, 114, 133, 140, 190, 210, 228, 266, 285, 380, 399, 420, 532, 570, 665, 798, 1140, 1330, 1596, 1995, 2660, 3990, 7980
The HCF of 418,7980 is 38.
Lets's calculate GCF of 418,7980
| 2 | 418, 7980 |
| 19 | 209, 3990 |
| 11, 210 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 418,7980 By Matching Biggest Common Factor Method
Now, list down the factors of 418
:1,2,11,19,22,38,209,418
Now, list down the factors of 7980
:1,2,3,4,5,6,7,10,12,14,15,19,20,21,28,30,35,38,42,57,60,70,76,84,95,105,114,133,140,190,210,228,266,285,380,399,420,532,570,665,798,1140,1330,1596,1995,2660,3990,7980
Greatest Common Factor
We found the factors 418,7980 . The biggest common factor number is the GCF number.
So the greatest common factor 418,7980 is 38.
Lets's calculate LCM of 252,210
| 2 | 252, 210 |
| 3 | 126, 105 |
| 7 | 42, 35 |
| 6, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 6 x 5 = 1260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/1260
Therefore, the GCF of Fractions 418/252,7980/210 is 38/1260
Least Common Multiple of 252,210 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 252,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(252,210) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(252,210) x common factors =42 x 1 = 42
LCM(252,210) = ( 252 × 210 ) / 42
LCM(252,210) = 52920 / 42
LCM(252,210) = 1260
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FAQs on GCF of Fractions of 418/252, 7980/210
1. What is the HCF of 418,7980?
The HCF of 418,7980 is 38
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 418/252, 7980/210?
Answer: GCF of Numerators as per given numbers 418/252, 7980/210 is
GCF of Numerators i.e. for 418,7980 is 38
LCM of denominators i.e. for 252,210 is 1260.
Thus, GCF of Fractions is 38/1260.Finally, GCF of Fractions for 418/252, 7980/210 is 38/1260.