GCF of 770/370, 1400/7540
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 770/370, 1400/7540 i.e 70/278980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/370, 1400/7540.
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 770/370,1400/7540?
Given fractions are 770/370,1400/7540
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 770/370,1400/7540, numerators are 770,1400
Denominators are 370,7540
The GCF of 770,1400 is 70 .
LCM of 370,7540 is 278980.
The greatest common factor of 770/370,1400/7540 = [GCF of 770,1400]/[LCM of 370,7540]= 70/278980
Therefore, the GCF of 770/370,1400/7540 is 70/278980.
To find the highest common factor of 770,1400, we have to find the factors of both numbers and list the highest common factor.
The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770
The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400
The HCF of 770,1400 is 70.
Lets's calculate GCF of 770,1400
| 2 | 770, 1400 |
| 5 | 385, 700 |
| 7 | 77, 140 |
| 11, 20 |
∴ So the GCF of the given numbers is 2 x 5 x 7 = 70
Greatest Common Factor of 770,1400 By Matching Biggest Common Factor Method
Now, list down the factors of 770
:1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770
Now, list down the factors of 1400
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,140,175,200,280,350,700,1400
Greatest Common Factor
We found the factors 770,1400 . The biggest common factor number is the GCF number.
So the greatest common factor 770,1400 is 70.
Lets's calculate LCM of 370,7540
| 2 | 370, 7540 |
| 5 | 185, 3770 |
| 37, 754 |
∴ So the LCM of the given numbers is 2 x 5 x 37 x 754 = 278980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/278980
Therefore, the GCF of Fractions 770/370,1400/7540 is 70/278980
Least Common Multiple of 370,7540 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 370,7540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(370,7540) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(370,7540) x common factors =10 x 1 = 10
LCM(370,7540) = ( 370 × 7540 ) / 10
LCM(370,7540) = 2789800 / 10
LCM(370,7540) = 278980
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FAQs on GCF of Fractions of 770/370, 1400/7540
1. What is the HCF of 770,1400?
The HCF of 770,1400 is 70
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 770/370, 1400/7540?
Answer: GCF of Numerators as per given numbers 770/370, 1400/7540 is
GCF of Numerators i.e. for 770,1400 is 70
LCM of denominators i.e. for 370,7540 is 278980.
Thus, GCF of Fractions is 70/278980.Finally, GCF of Fractions for 770/370, 1400/7540 is 70/278980.