What is GCF of 12 and 34?

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GCF of 12 and 34 is 2

How to find GCF of two numbers

Steps to find GCF of 12 and 34

Find all the numbers that would divide 12 and 34 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 12 and 34, and read off the answer!

Example: Find gcf of 12 and 34

Factors for 12: 1, 2, 3, 4, 6, 12
Factors for 34: 1, 2, 17, 34

Hence, GCf of 12 and 34 is 2

How do we define GCF?

In mathematics we use GCF or greatest common method to find out the greatest possible positive integer which can completely divide the given numbers. It is written as GCF (12, 34).

Properties of GCF

The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 12 and 34 is 2, where 2 is less than both 12 and 34.
GCF of two consecutive numbers is always 1.
The product of GCF and LCM of two given numbers is equal to the product of two numbers.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of Factors

Each number is a factor of itself. Eg. 12 and 34 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 12 and also of 34.
Every number is a factor of zero (0), since 12 x 0 = 0 and 34 x 0 = 0.
Every number other than 1 has at least two factors, namely the number itself and 1.
Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 12 are exact divisors of 12 and 1, 2, 17, 34 are exact divisors of 34.
Factors of 12 are 1, 2, 3, 4, 6, 12. Each factor divides 12 without leaving a remainder.
Simlarly, factors of 34 are 1, 2, 17, 34. Each factor divides 34 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12 are all less than or equal to 12 and 1, 2, 17, 34 are all less than or equal to 34.

Steps to find Factors of 12 and 34

Step 1. Find all the numbers that would divide 12 and 34 without leaving any remainder. Starting with the number 1 upto 6 (half of 12) and 1 upto 17 (half of 34). The number 1 and the number itself are always factors of the given number.

12 ÷ 1 : Remainder = 0

34 ÷ 1 : Remainder = 0

12 ÷ 2 : Remainder = 0

34 ÷ 2 : Remainder = 0

12 ÷ 3 : Remainder = 0

34 ÷ 17 : Remainder = 0

12 ÷ 4 : Remainder = 0

34 ÷ 34 : Remainder = 0

12 ÷ 6 : Remainder = 0

12 ÷ 12 : Remainder = 0

Hence, Factors of 12 are 1, 2, 3, 4, 6, and 12

And, Factors of 34 are 1, 2, 17, and 34

Examples of GCF

Sammy baked 12 chocolate cookies and 34 fruit and nut cookies to package in plastic containers for her friends at college. She wants to divide the cookies into identical boxes so that each box has the same number of each kind of cookies. She wishes that each box should have greatest number of cookies possible, how many plastic boxes does she need?

Since Sammy wants to pack greatest number of cookies possible. So for calculating total number of boxes required we need to calculate the GCF of 12 and 34.
GCF of 12 and 34 is 2.

A class has 12 boys and 34 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?

To find the greatest number of students that could be in each row, we need to find the GCF of 12 and 34. Hence, GCF of 12 and 34 is 2.

What is the difference between GCF and LCM?

Major and simple difference betwen GCF and LCM is that GCF gives you the greatest common factor while LCM finds out the least common factor possible for the given numbers.

Ram has 12 cans of Pepsi and 34 cans of Coca Cola. He wants to create identical refreshment tables that will be organized in his house warming party. He also doesn't want to have any can left over. What is the greatest number of tables that Ram can arrange?

To find the greatest number of tables that Ram can stock we need to find the GCF of 12 and 34. Hence GCF of 12 and 34 is 2. So the number of tables that can be arranged is 2.

Ariel is making ready to eat meals to share with friends. She has 12 bottles of water and 34 cans of food, which she would like to distribute equally, with no left overs. What is the greatest number of boxes Ariel can make?

The greatest number of boxes Ariel can make would be equal to GCF of 12 and 34. So the GCF of 12 and 34 is 2.

Mary has 12 blue buttons and 34 white buttons. She wants to place them in identical groups without any buttons left, in the greatest way possible. Can you help Mary arranging them in groups?

Greatest possible way in which Mary can arrange them in groups would be GCF of 12 and 34. Hence, the GCF of 12 and 34 or the greatest arrangement is 2.

Kamal is making identical balloon arrangements for a party. He has 12 maroon balloons, and 34 orange balloons. He wants each arrangement tohave the same number of each color. What is the greatest number of arrangements that he can make if every balloon is used?

The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 12 and 34. So the GCF of 12 and 34 is 2.

Kunal is making baskets full of nuts and dried fruits. He has 12 bags of nuts and 34 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?

the greatest number of baskets that Kunal can make would be equal to GCF of 12 and 34. So the GCF of 12 and 34 is 2.

To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 12 bus tickets and 34 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?

To make the greatest number of envelopes Abir needs to find out the GCF of 12 and 34. Hence, GCF of 12 and 34 is 2.