What is GCF of 42 and 105?

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GCF of 42 and 105 is 21

How to find GCF of two numbers

Steps to find GCF of 42 and 105

Find all the numbers that would divide 42 and 105 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 42 and 105, and read off the answer!

Example: Find gcf of 42 and 105

Factors for 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors for 105: 1, 3, 5, 7, 15, 21, 35, 105

Hence, GCf of 42 and 105 is 21

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, 105).

Properties of GCF

Given two numbers 42 and 105, such that GCF is 21 where 21 will always be less than 42 and 105.
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 105 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, 3, 5, 7, 15, 21, 35, 105 are exact divisors of 105.
1 is a factor of every number. Eg. 1 is a factor of 42 and also of 105.
Every number is a factor of zero (0), since 42 x 0 = 0 and 105 x 0 = 0.

Steps to find Factors of 42 and 105

Step 1. Find all the numbers that would divide 42 and 105 without leaving any remainder. Starting with the number 1 upto 21 (half of 42) and 1 upto 52 (half of 105). The number 1 and the number itself are always factors of the given number.

42 ÷ 1 : Remainder = 0

105 ÷ 1 : Remainder = 0

42 ÷ 2 : Remainder = 0

105 ÷ 3 : Remainder = 0

42 ÷ 3 : Remainder = 0

105 ÷ 5 : Remainder = 0

42 ÷ 6 : Remainder = 0

105 ÷ 7 : Remainder = 0

42 ÷ 7 : Remainder = 0

105 ÷ 15 : Remainder = 0

42 ÷ 14 : Remainder = 0

105 ÷ 21 : Remainder = 0

42 ÷ 21 : Remainder = 0

105 ÷ 35 : Remainder = 0

42 ÷ 42 : Remainder = 0

105 ÷ 105 : Remainder = 0

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

And, Factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105

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, 105) = ( 42 * 105 ) / LCM(42, 105) = 21.

What is the GCF of 42 and 105?

GCF of 42 and 105 is 21.

Ram has 42 cans of Pepsi and 105 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 105. Hence GCF of 42 and 105 is 21. So the number of tables that can be arranged is 21.

Rubel is creating individual servings of starters for her birthday party. He has 42 pizzas and 105 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 105. Thus GCF of 42 and 105 is 21.

Ariel is making ready to eat meals to share with friends. She has 42 bottles of water and 105 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 105. So the GCF of 42 and 105 is 21.

Mary has 42 blue buttons and 105 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 105. Hence, the GCF of 42 and 105 or the greatest arrangement is 21.

Kamal is making identical balloon arrangements for a party. He has 42 maroon balloons, and 105 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 105. So the GCF of 42 and 105 is 21.

Kunal is making baskets full of nuts and dried fruits. He has 42 bags of nuts and 105 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 105. So the GCF of 42 and 105 is 21.

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 105 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 105. Hence, GCF of 42 and 105 is 21.