GCF of 624/420, 6837/690
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 624/420, 6837/690 i.e 3/9660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 624/420, 6837/690.
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 624/420,6837/690?
Given fractions are 624/420,6837/690
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 624/420,6837/690, numerators are 624,6837
Denominators are 420,690
The GCF of 624,6837 is 3 .
LCM of 420,690 is 9660.
The greatest common factor of 624/420,6837/690 = [GCF of 624,6837]/[LCM of 420,690]= 3/9660
Therefore, the GCF of 624/420,6837/690 is 3/9660.
To find the highest common factor of 624,6837, we have to find the factors of both numbers and list the highest common factor.
The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
The factors of 6837 are 1, 3, 43, 53, 129, 159, 2279, 6837
The HCF of 624,6837 is 3.
Lets's calculate GCF of 624,6837
| 3 | 624, 6837 |
| 208, 2279 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 624,6837 By Matching Biggest Common Factor Method
Now, list down the factors of 624
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Now, list down the factors of 6837
:1,3,43,53,129,159,2279,6837
Greatest Common Factor
We found the factors 624,6837 . The biggest common factor number is the GCF number.
So the greatest common factor 624,6837 is 3.
Lets's calculate LCM of 420,690
| 2 | 420, 690 |
| 3 | 210, 345 |
| 5 | 70, 115 |
| 14, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 14 x 23 = 9660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/9660
Therefore, the GCF of Fractions 624/420,6837/690 is 3/9660
Least Common Multiple of 420,690 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 420,690 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,690) = 30
common factors(in case of two or more numbers have common factors) = 1
GCF(420,690) x common factors =30 x 1 = 30
LCM(420,690) = ( 420 × 690 ) / 30
LCM(420,690) = 289800 / 30
LCM(420,690) = 9660
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FAQs on GCF of Fractions of 624/420, 6837/690
1. What is the HCF of 624,6837?
The HCF of 624,6837 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 624/420, 6837/690?
Answer: GCF of Numerators as per given numbers 624/420, 6837/690 is
GCF of Numerators i.e. for 624,6837 is 3
LCM of denominators i.e. for 420,690 is 9660.
Thus, GCF of Fractions is 3/9660.Finally, GCF of Fractions for 624/420, 6837/690 is 3/9660.