GCF of 1824/274, 1770/7074
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1824/274, 1770/7074 i.e 6/969138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1824/274, 1770/7074.
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 1824/274,1770/7074?
Given fractions are 1824/274,1770/7074
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 1824/274,1770/7074, numerators are 1824,1770
Denominators are 274,7074
The GCF of 1824,1770 is 6 .
LCM of 274,7074 is 969138.
The greatest common factor of 1824/274,1770/7074 = [GCF of 1824,1770]/[LCM of 274,7074]= 6/969138
Therefore, the GCF of 1824/274,1770/7074 is 6/969138.
To find the highest common factor of 1824,1770, we have to find the factors of both numbers and list the highest common factor.
The factors of 1824 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824
The factors of 1770 are 1, 2, 3, 5, 6, 10, 15, 30, 59, 118, 177, 295, 354, 590, 885, 1770
The HCF of 1824,1770 is 6.
Lets's calculate GCF of 1824,1770
| 2 | 1824, 1770 |
| 3 | 912, 885 |
| 304, 295 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 1824,1770 By Matching Biggest Common Factor Method
Now, list down the factors of 1824
:1,2,3,4,6,8,12,16,19,24,32,38,48,57,76,96,114,152,228,304,456,608,912,1824
Now, list down the factors of 1770
:1,2,3,5,6,10,15,30,59,118,177,295,354,590,885,1770
Greatest Common Factor
We found the factors 1824,1770 . The biggest common factor number is the GCF number.
So the greatest common factor 1824,1770 is 6.
Lets's calculate LCM of 274,7074
| 2 | 274, 7074 |
| 137, 3537 |
∴ So the LCM of the given numbers is 2 x 137 x 3537 = 969138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/969138
Therefore, the GCF of Fractions 1824/274,1770/7074 is 6/969138
Least Common Multiple of 274,7074 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 274,7074 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,7074) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,7074) x common factors =2 x 1 = 2
LCM(274,7074) = ( 274 × 7074 ) / 2
LCM(274,7074) = 1938276 / 2
LCM(274,7074) = 969138
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FAQs on GCF of Fractions of 1824/274, 1770/7074
1. What is the HCF of 1824,1770?
The HCF of 1824,1770 is 6
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 1824/274, 1770/7074?
Answer: GCF of Numerators as per given numbers 1824/274, 1770/7074 is
GCF of Numerators i.e. for 1824,1770 is 6
LCM of denominators i.e. for 274,7074 is 969138.
Thus, GCF of Fractions is 6/969138.Finally, GCF of Fractions for 1824/274, 1770/7074 is 6/969138.