GCF of 3178/727, 3480/7267
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3178/727, 3480/7267 i.e 2/5283109 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3178/727, 3480/7267.
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 3178/727,3480/7267?
Given fractions are 3178/727,3480/7267
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 3178/727,3480/7267, numerators are 3178,3480
Denominators are 727,7267
The GCF of 3178,3480 is 2 .
LCM of 727,7267 is 5283109.
The greatest common factor of 3178/727,3480/7267 = [GCF of 3178,3480]/[LCM of 727,7267]= 2/5283109
Therefore, the GCF of 3178/727,3480/7267 is 2/5283109.
To find the highest common factor of 3178,3480, we have to find the factors of both numbers and list the highest common factor.
The factors of 3178 are 1, 2, 7, 14, 227, 454, 1589, 3178
The factors of 3480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 29, 30, 40, 58, 60, 87, 116, 120, 145, 174, 232, 290, 348, 435, 580, 696, 870, 1160, 1740, 3480
The HCF of 3178,3480 is 2.
Lets's calculate GCF of 3178,3480
| 2 | 3178, 3480 |
| 1589, 1740 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3178,3480 By Matching Biggest Common Factor Method
Now, list down the factors of 3178
:1,2,7,14,227,454,1589,3178
Now, list down the factors of 3480
:1,2,3,4,5,6,8,10,12,15,20,24,29,30,40,58,60,87,116,120,145,174,232,290,348,435,580,696,870,1160,1740,3480
Greatest Common Factor
We found the factors 3178,3480 . The biggest common factor number is the GCF number.
So the greatest common factor 3178,3480 is 2.
Lets's calculate LCM of 727,7267
Given numbers has no common factors except 1. So, there LCM is their product i.e 5283109
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5283109
Therefore, the GCF of Fractions 3178/727,3480/7267 is 2/5283109
Least Common Multiple of 727,7267 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 727,7267 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(727,7267) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(727,7267) x common factors =1 x 1 = 1
LCM(727,7267) = ( 727 × 7267 ) / 1
LCM(727,7267) = 5283109 / 1
LCM(727,7267) = 5283109
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FAQs on GCF of Fractions of 3178/727, 3480/7267
1. What is the HCF of 3178,3480?
The HCF of 3178,3480 is 2
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 3178/727, 3480/7267?
Answer: GCF of Numerators as per given numbers 3178/727, 3480/7267 is
GCF of Numerators i.e. for 3178,3480 is 2
LCM of denominators i.e. for 727,7267 is 5283109.
Thus, GCF of Fractions is 2/5283109.Finally, GCF of Fractions for 3178/727, 3480/7267 is 2/5283109.