Get help with finding GCF of fractions 16/30, 24/60, 32/75, 36/120 using GCF of Fractions Calculator to know the result 4/600 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 16/30, 24/60, 32/75, 36/120 is **4/600**.

GCF(16/30, 24/60, 32/75, 36/120) = 4/600

Enter two or more fractions separated by **"commas"**

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

Given fractions are 16/30,24/60,32/75,36/120

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 16,24,32,36

Greatest Common Factor of Numerators i.e. GCF of 16,24,32,36 is 4 .

LCM of Denominators means LCM of 30,60,75,120 as per the given fractions.

LCM of 30,60,75,120 is 600 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 16,24,32,36

2 | 16, 24, 32, 36 |

2 | 8, 12, 16, 18 |

4, 6, 8, 9 |

∴ So the GCF of the given numbers is 2 x 2 = 4

**Factors of 16**

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

**Factors of 24**

List of positive integer factors of 24 that divides 24 without a remainder.

1,2,3,4,6,8,12,24

**Factors of 32**

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

**Factors of 36**

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

**Greatest Common Factor**

We found the factors 16,24,32,36 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 16,24,32,36 ** is **4**.

Lets's calculate LCM of 30,60,75,120

2 | 30, 60, 75, 120 |

2 | 15, 30, 75, 60 |

3 | 15, 15, 75, 30 |

5 | 5, 5, 25, 10 |

1, 1, 5, 2 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 1 x 5 x 2 = 600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/600

Therefore, the GCF of Fractions 16/30,24/60,32/75,36/120 is 4/600

The formula of **LCM** is LCM(a_{1},a_{2},a_{3}....,a_{n}) = ( a_{1} × a_{2} × a_{3} × .... × a_{n}) / GCF(a_{1},a_{2},a_{3}....,a_{n}) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 30,60,75,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,60,75,120) = 15

common factors(in case of two or more numbers have common factors) = 1800

GCF(30,60,75,120) x common factors =15 x 1800 = 27000

LCM(30,60,75,120) = ( 30 × 60 × 75 × 120 ) / 27000

LCM(30,60,75,120) = 16200000 / 27000

LCM(30,60,75,120) = 600

Here are some samples of GCF of Fractions calculations.

1. 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.

2. What is the GCF of Fractions for 16/30, 24/60, 32/75, 36/120?

Answer: GCF of Numerators as per given numbers 16/30, 24/60, 32/75, 36/120 is

GCF of Numerators i.e. for 16,24,32,36 is 4

LCM of denominators i.e. for 30,60,75,120 is 600.

Thus, GCF of Fractions is 4/600.Finally, GCF of Fractions for 16/30, 24/60, 32/75, 36/120 is 4/600.