GCF of 1738/174, 7140/1065
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1738/174, 7140/1065 i.e 2/61770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1738/174, 7140/1065.
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 1738/174,7140/1065?
Given fractions are 1738/174,7140/1065
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 1738/174,7140/1065, numerators are 1738,7140
Denominators are 174,1065
The GCF of 1738,7140 is 2 .
LCM of 174,1065 is 61770.
The greatest common factor of 1738/174,7140/1065 = [GCF of 1738,7140]/[LCM of 174,1065]= 2/61770
Therefore, the GCF of 1738/174,7140/1065 is 2/61770.
To find the highest common factor of 1738,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 1738 are 1, 2, 11, 22, 79, 158, 869, 1738
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The HCF of 1738,7140 is 2.
Lets's calculate GCF of 1738,7140
| 2 | 1738, 7140 |
| 869, 3570 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1738,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 1738
:1,2,11,22,79,158,869,1738
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Greatest Common Factor
We found the factors 1738,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 1738,7140 is 2.
Lets's calculate LCM of 174,1065
| 3 | 174, 1065 |
| 58, 355 |
∴ So the LCM of the given numbers is 3 x 58 x 355 = 61770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/61770
Therefore, the GCF of Fractions 1738/174,7140/1065 is 2/61770
Least Common Multiple of 174,1065 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 174,1065 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,1065) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(174,1065) x common factors =3 x 1 = 3
LCM(174,1065) = ( 174 × 1065 ) / 3
LCM(174,1065) = 185310 / 3
LCM(174,1065) = 61770
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FAQs on GCF of Fractions of 1738/174, 7140/1065
1. What is the HCF of 1738,7140?
The HCF of 1738,7140 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 1738/174, 7140/1065?
Answer: GCF of Numerators as per given numbers 1738/174, 7140/1065 is
GCF of Numerators i.e. for 1738,7140 is 2
LCM of denominators i.e. for 174,1065 is 61770.
Thus, GCF of Fractions is 2/61770.Finally, GCF of Fractions for 1738/174, 7140/1065 is 2/61770.