GCF of 1274/174, 1960/7080
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1274/174, 1960/7080 i.e 98/205320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1274/174, 1960/7080.
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 1274/174,1960/7080?
Given fractions are 1274/174,1960/7080
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 1274/174,1960/7080, numerators are 1274,1960
Denominators are 174,7080
The GCF of 1274,1960 is 98 .
LCM of 174,7080 is 205320.
The greatest common factor of 1274/174,1960/7080 = [GCF of 1274,1960]/[LCM of 174,7080]= 98/205320
Therefore, the GCF of 1274/174,1960/7080 is 98/205320.
To find the highest common factor of 1274,1960, we have to find the factors of both numbers and list the highest common factor.
The factors of 1274 are 1, 2, 7, 13, 14, 26, 49, 91, 98, 182, 637, 1274
The factors of 1960 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960
The HCF of 1274,1960 is 98.
Lets's calculate GCF of 1274,1960
| 2 | 1274, 1960 |
| 7 | 637, 980 |
| 7 | 91, 140 |
| 13, 20 |
∴ So the GCF of the given numbers is 2 x 7 x 7 = 98
Greatest Common Factor of 1274,1960 By Matching Biggest Common Factor Method
Now, list down the factors of 1274
:1,2,7,13,14,26,49,91,98,182,637,1274
Now, list down the factors of 1960
:1,2,4,5,7,8,10,14,20,28,35,40,49,56,70,98,140,196,245,280,392,490,980,1960
Greatest Common Factor
We found the factors 1274,1960 . The biggest common factor number is the GCF number.
So the greatest common factor 1274,1960 is 98.
Lets's calculate LCM of 174,7080
| 2 | 174, 7080 |
| 3 | 87, 3540 |
| 29, 1180 |
∴ So the LCM of the given numbers is 2 x 3 x 29 x 1180 = 205320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 98/205320
Therefore, the GCF of Fractions 1274/174,1960/7080 is 98/205320
Least Common Multiple of 174,7080 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 174,7080 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,7080) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(174,7080) x common factors =6 x 1 = 6
LCM(174,7080) = ( 174 × 7080 ) / 6
LCM(174,7080) = 1231920 / 6
LCM(174,7080) = 205320
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FAQs on GCF of Fractions of 1274/174, 1960/7080
1. What is the HCF of 1274,1960?
The HCF of 1274,1960 is 98
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 1274/174, 1960/7080?
Answer: GCF of Numerators as per given numbers 1274/174, 1960/7080 is
GCF of Numerators i.e. for 1274,1960 is 98
LCM of denominators i.e. for 174,7080 is 205320.
Thus, GCF of Fractions is 98/205320.Finally, GCF of Fractions for 1274/174, 1960/7080 is 98/205320.