GCF of 1869/274, 7224/5100
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1869/274, 7224/5100 i.e 21/698700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1869/274, 7224/5100.
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 1869/274,7224/5100?
Given fractions are 1869/274,7224/5100
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 1869/274,7224/5100, numerators are 1869,7224
Denominators are 274,5100
The GCF of 1869,7224 is 21 .
LCM of 274,5100 is 698700.
The greatest common factor of 1869/274,7224/5100 = [GCF of 1869,7224]/[LCM of 274,5100]= 21/698700
Therefore, the GCF of 1869/274,7224/5100 is 21/698700.
To find the highest common factor of 1869,7224, we have to find the factors of both numbers and list the highest common factor.
The factors of 1869 are 1, 3, 7, 21, 89, 267, 623, 1869
The factors of 7224 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 43, 56, 84, 86, 129, 168, 172, 258, 301, 344, 516, 602, 903, 1032, 1204, 1806, 2408, 3612, 7224
The HCF of 1869,7224 is 21.
Lets's calculate GCF of 1869,7224
| 3 | 1869, 7224 |
| 7 | 623, 2408 |
| 89, 344 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 1869,7224 By Matching Biggest Common Factor Method
Now, list down the factors of 1869
:1,3,7,21,89,267,623,1869
Now, list down the factors of 7224
:1,2,3,4,6,7,8,12,14,21,24,28,42,43,56,84,86,129,168,172,258,301,344,516,602,903,1032,1204,1806,2408,3612,7224
Greatest Common Factor
We found the factors 1869,7224 . The biggest common factor number is the GCF number.
So the greatest common factor 1869,7224 is 21.
Lets's calculate LCM of 274,5100
| 2 | 274, 5100 |
| 137, 2550 |
∴ So the LCM of the given numbers is 2 x 137 x 2550 = 698700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/698700
Therefore, the GCF of Fractions 1869/274,7224/5100 is 21/698700
Least Common Multiple of 274,5100 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 274,5100 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,5100) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,5100) x common factors =2 x 1 = 2
LCM(274,5100) = ( 274 × 5100 ) / 2
LCM(274,5100) = 1397400 / 2
LCM(274,5100) = 698700
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FAQs on GCF of Fractions of 1869/274, 7224/5100
1. What is the HCF of 1869,7224?
The HCF of 1869,7224 is 21
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 1869/274, 7224/5100?
Answer: GCF of Numerators as per given numbers 1869/274, 7224/5100 is
GCF of Numerators i.e. for 1869,7224 is 21
LCM of denominators i.e. for 274,5100 is 698700.
Thus, GCF of Fractions is 21/698700.Finally, GCF of Fractions for 1869/274, 7224/5100 is 21/698700.