What is GCF of 63 and 105?

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GCF of 63 and 105 is 21

How to find GCF of two numbers

Steps to find GCF of 63 and 105

Find all the numbers that would divide 63 and 105 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 63 and 105, and read off the answer!

Example: Find gcf of 63 and 105

Factors for 63: 1, 3, 7, 9, 21, 63
Factors for 105: 1, 3, 5, 7, 15, 21, 35, 105

Hence, GCf of 63 and 105 is 21

What does GCF mean in mathematics?

Greatest Common Fcator (GCF) or also sometimes written as greates common divisor is the largest number that can evenly divide the given two numbers. GCF is represented as GCF (63, 105).

Properties of GCF

The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
GCF of two consecutive numbers is always 1.
Given two numbers 63 and 105, such that GCF is 21 where 21 will always be less than 63 and 105.
Product of two numbers is always equal to the product of their GCF and LCM.

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of Factors

Every number is a factor of zero (0), since 63 x 0 = 0 and 105 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, 3, 7, 9, 21, 63 are exact divisors of 63 and 1, 3, 5, 7, 15, 21, 35, 105 are exact divisors of 105.
Factors of 63 are 1, 3, 7, 9, 21, 63. Each factor divides 63 without leaving a remainder.
Simlarly, factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. Each factor divides 105 without leaving a remainder.

Steps to find Factors of 63 and 105

Step 1. Find all the numbers that would divide 63 and 105 without leaving any remainder. Starting with the number 1 upto 31 (half of 63) and 1 upto 52 (half of 105). The number 1 and the number itself are always factors of the given number.

63 ÷ 1 : Remainder = 0

105 ÷ 1 : Remainder = 0

63 ÷ 3 : Remainder = 0

105 ÷ 3 : Remainder = 0

63 ÷ 7 : Remainder = 0

105 ÷ 5 : Remainder = 0

63 ÷ 9 : Remainder = 0

105 ÷ 7 : Remainder = 0

63 ÷ 21 : Remainder = 0

105 ÷ 15 : Remainder = 0

63 ÷ 63 : Remainder = 0

105 ÷ 21 : Remainder = 0

105 ÷ 35 : Remainder = 0

105 ÷ 105 : Remainder = 0

Hence, Factors of 63 are 1, 3, 7, 9, 21, and 63

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

Examples of GCF

Sammy baked 63 chocolate cookies and 105 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 63 and 105.
GCF of 63 and 105 is 21.

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.

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

GCF and LCM of two numbers can be related as GCF(63, 105) = ( 63 * 105 ) / LCM(63, 105) = 21.

What is the GCF of 63 and 105?

GCF of 63 and 105 is 21.

Ram has 63 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 63 and 105. Hence GCF of 63 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 63 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 63 and 105. Thus GCF of 63 and 105 is 21.

Ariel is making ready to eat meals to share with friends. She has 63 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 63 and 105. So the GCF of 63 and 105 is 21.

Mary has 63 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 63 and 105. Hence, the GCF of 63 and 105 or the greatest arrangement is 21.

Kamal is making identical balloon arrangements for a party. He has 63 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 63 and 105. So the GCF of 63 and 105 is 21.