What is GCF of 45 and 105?

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GCF of 45 and 105 is 15

How to find GCF of two numbers

Steps to find GCF of 45 and 105

Find all the numbers that would divide 45 and 105 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 45 and 105, and read off the answer!

Example: Find gcf of 45 and 105

Factors for 45: 1, 3, 5, 9, 15, 45
Factors for 105: 1, 3, 5, 7, 15, 21, 35, 105

Hence, GCf of 45 and 105 is 15

Definition of GCF

Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (45, 105).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 45 and 105 is 15, where 15 is less than both the numbers.
If the given numbers are consecutive than GCF is always 1.
Product of two numbers is always equal to the product of their GCF and LCM.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of Factors

Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 45 are exact divisors of 45 and 1, 3, 5, 7, 15, 21, 35, 105 are exact divisors of 105.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 45 and 105 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 45 and also of 105.

Steps to find Factors of 45 and 105

Step 1. Find all the numbers that would divide 45 and 105 without leaving any remainder. Starting with the number 1 upto 22 (half of 45) and 1 upto 52 (half of 105). The number 1 and the number itself are always factors of the given number.

45 ÷ 1 : Remainder = 0

105 ÷ 1 : Remainder = 0

45 ÷ 3 : Remainder = 0

105 ÷ 3 : Remainder = 0

45 ÷ 5 : Remainder = 0

105 ÷ 5 : Remainder = 0

45 ÷ 9 : Remainder = 0

105 ÷ 7 : Remainder = 0

45 ÷ 15 : Remainder = 0

105 ÷ 15 : Remainder = 0

45 ÷ 45 : Remainder = 0

105 ÷ 21 : Remainder = 0

105 ÷ 35 : Remainder = 0

105 ÷ 105 : Remainder = 0

Hence, Factors of 45 are 1, 3, 5, 9, 15, and 45

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

Examples of GCF

Sammy baked 45 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 45 and 105.
GCF of 45 and 105 is 15.

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(45, 105) = ( 45 * 105 ) / LCM(45, 105) = 15.

What is the GCF of 45 and 105?

GCF of 45 and 105 is 15.

Ram has 45 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 45 and 105. Hence GCF of 45 and 105 is 15. So the number of tables that can be arranged is 15.

Rubel is creating individual servings of starters for her birthday party. He has 45 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 45 and 105. Thus GCF of 45 and 105 is 15.

Ariel is making ready to eat meals to share with friends. She has 45 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 45 and 105. So the GCF of 45 and 105 is 15.

Mary has 45 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 45 and 105. Hence, the GCF of 45 and 105 or the greatest arrangement is 15.

Kamal is making identical balloon arrangements for a party. He has 45 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 45 and 105. So the GCF of 45 and 105 is 15.