# What is GCF of 42 and 72?

GCF of 42 and 72 is 6

#### How to find GCF of two numbers

 1.   Steps to find GCF of 42 and 72 2.   What is GCF of two numbers? 3.   What are Factors? 4.   Examples of GCF

### Example: Find gcf of 42 and 72

• Factors for 42: 1, 2, 3, 6, 7, 14, 21, 42
• Factors for 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Hence, GCf of 42 and 72 is 6

#### 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 (42, 72).

#### Properties of GCF

• Given two numbers 42 and 72, such that GCF is 6 where 6 will always be less than 42 and 72.
• GCF of two numbers is always equal to 1 in case given numbers are consecutive.
• The product of GCF and LCM of two given numbers is equal to the product of two numbers.
• The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.

#### 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. 42 and 72 are factors of themselves respectively.
• 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, 6, 7, 14, 21, 42 are exact divisors of 42 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are exact divisors of 72.
• 1 is a factor of every number. Eg. 1 is a factor of 42 and also of 72.
• Every number is a factor of zero (0), since 42 x 0 = 0 and 72 x 0 = 0.

#### Steps to find Factors of 42 and 72

• Step 1. Find all the numbers that would divide 42 and 72 without leaving any remainder. Starting with the number 1 upto 21 (half of 42) and 1 upto 36 (half of 72). The number 1 and the number itself are always factors of the given number.
42 ÷ 1 : Remainder = 0
72 ÷ 1 : Remainder = 0
42 ÷ 2 : Remainder = 0
72 ÷ 2 : Remainder = 0
42 ÷ 3 : Remainder = 0
72 ÷ 3 : Remainder = 0
42 ÷ 6 : Remainder = 0
72 ÷ 4 : Remainder = 0
42 ÷ 7 : Remainder = 0
72 ÷ 6 : Remainder = 0
42 ÷ 14 : Remainder = 0
72 ÷ 8 : Remainder = 0
42 ÷ 21 : Remainder = 0
72 ÷ 9 : Remainder = 0
42 ÷ 42 : Remainder = 0
72 ÷ 12 : Remainder = 0
72 ÷ 18 : Remainder = 0
72 ÷ 24 : Remainder = 0
72 ÷ 36 : Remainder = 0
72 ÷ 72 : Remainder = 0

Hence, Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42

And, Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

#### Examples of GCF

What is the relation between LCM and GCF (Greatest Common Factor)?

GCF and LCM of two numbers can be related as GCF(42, 72) = ( 42 * 72 ) / LCM(42, 72) = 6.

What is the GCF of 42 and 72?

GCF of 42 and 72 is 6.

Ram has 42 cans of Pepsi and 72 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 42 and 72. Hence GCF of 42 and 72 is 6. So the number of tables that can be arranged is 6.

Rubel is creating individual servings of starters for her birthday party. He has 42 pizzas and 72 hamburgers. He wants each serving to be identical, with no left overs. Can you help Rubel in arranging the same in greatest possible way?

The greatest number of servings Rubel can create would be equal to the GCF of 42 and 72. Thus GCF of 42 and 72 is 6.

Ariel is making ready to eat meals to share with friends. She has 42 bottles of water and 72 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 42 and 72. So the GCF of 42 and 72 is 6.

Mary has 42 blue buttons and 72 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 42 and 72. Hence, the GCF of 42 and 72 or the greatest arrangement is 6.

Kamal is making identical balloon arrangements for a party. He has 42 maroon balloons, and 72 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 42 and 72. So the GCF of 42 and 72 is 6.

Kunal is making baskets full of nuts and dried fruits. He has 42 bags of nuts and 72 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 42 and 72. So the GCF of 42 and 72 is 6.

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 42 bus tickets and 72 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 42 and 72. Hence, GCF of 42 and 72 is 6.