GCF of 77/66, 38/55, 29/40, 84/32
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 77/66, 38/55, 29/40, 84/32 i.e 1/5280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/66, 38/55, 29/40, 84/32.
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 77/66,38/55,29/40,84/32?
Given fractions are 77/66,38/55,29/40,84/32
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 77/66,38/55,29/40,84/32, numerators are 77,38,29,84
Denominators are 66,55,40,32
The GCF of 77,38,29,84 is 1 .
LCM of 66,55,40,32 is 5280.
The greatest common factor of 77/66,38/55,29/40,84/32 = [GCF of 77,38,29,84]/[LCM of 66,55,40,32]= 1/5280
Therefore, the GCF of 77/66,38/55,29/40,84/32 is 1/5280.
To find the highest common factor of 77,38,29,84, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 38 are 1, 2, 19, 38
The factors of 29 are 1, 29
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The HCF of 77,38,29,84 is 1.
Lets's calculate GCF of 77,38,29,84
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 77,38,29,84 By Matching Biggest Common Factor Method
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 29
:1,29
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Greatest Common Factor
We found the factors 77,38,29,84 . The biggest common factor number is the GCF number.
So the greatest common factor 77,38,29,84 is 1.
Lets's calculate LCM of 66,55,40,32
| 2 | 66, 55, 40, 32 |
| 2 | 33, 55, 20, 16 |
| 2 | 33, 55, 10, 8 |
| 5 | 33, 55, 5, 4 |
| 11 | 33, 11, 1, 4 |
| 3, 1, 1, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 11 x 3 x 1 x 1 x 4 = 5280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5280
Therefore, the GCF of Fractions 77/66,38/55,29/40,84/32 is 1/5280
Least Common Multiple of 66,55,40,32 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 66,55,40,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,55,40,32) = 1
common factors(in case of two or more numbers have common factors) = 880
GCF(66,55,40,32) x common factors =1 x 880 = 880
LCM(66,55,40,32) = ( 66 × 55 × 40 × 32 ) / 880
LCM(66,55,40,32) = 4646400 / 880
LCM(66,55,40,32) = 5280
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 77/66, 38/55, 29/40, 84/32
1. What is the HCF of 77,38,29,84?
The HCF of 77,38,29,84 is 1
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 77/66, 38/55, 29/40, 84/32?
Answer: GCF of Numerators as per given numbers 77/66, 38/55, 29/40, 84/32 is
GCF of Numerators i.e. for 77,38,29,84 is 1
LCM of denominators i.e. for 66,55,40,32 is 5280.
Thus, GCF of Fractions is 1/5280.Finally, GCF of Fractions for 77/66, 38/55, 29/40, 84/32 is 1/5280.