# What is GCF of 32 and 45?

GCF of 32 and 45 is 1

#### How to find GCF of two numbers

 1.   Steps to find GCF of 32 and 45 2.   What is GCF of two numbers? 3.   What are Factors? 4.   Examples of GCF

### Example: Find gcf of 32 and 45

• Factors for 32: 1, 2, 4, 8, 16, 32
• Factors for 45: 1, 3, 5, 9, 15, 45

Hence, GCf of 32 and 45 is 1

#### 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 (32, 45).

#### Properties of GCF

• The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 32 and 45 is 1, where 1 is less than both 32 and 45.
• 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. 32 and 45 are factors of themselves respectively.
• 1 is a factor of every number. Eg. 1 is a factor of 32 and also of 45.
• Every number is a factor of zero (0), since 32 x 0 = 0 and 45 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, 4, 8, 16, 32 are exact divisors of 32 and 1, 3, 5, 9, 15, 45 are exact divisors of 45.
• Factors of 32 are 1, 2, 4, 8, 16, 32. Each factor divides 32 without leaving a remainder.
Simlarly, factors of 45 are 1, 3, 5, 9, 15, 45. Each factor divides 45 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32 are all less than or equal to 32 and 1, 3, 5, 9, 15, 45 are all less than or equal to 45.

#### Steps to find Factors of 32 and 45

• Step 1. Find all the numbers that would divide 32 and 45 without leaving any remainder. Starting with the number 1 upto 16 (half of 32) and 1 upto 22 (half of 45). The number 1 and the number itself are always factors of the given number.
32 ÷ 1 : Remainder = 0
45 ÷ 1 : Remainder = 0
32 ÷ 2 : Remainder = 0
45 ÷ 3 : Remainder = 0
32 ÷ 4 : Remainder = 0
45 ÷ 5 : Remainder = 0
32 ÷ 8 : Remainder = 0
45 ÷ 9 : Remainder = 0
32 ÷ 16 : Remainder = 0
45 ÷ 15 : Remainder = 0
32 ÷ 32 : Remainder = 0
45 ÷ 45 : Remainder = 0

Hence, Factors of 32 are 1, 2, 4, 8, 16, and 32

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

#### Examples of GCF

Sammy baked 32 chocolate cookies and 45 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 32 and 45.
GCF of 32 and 45 is 1.

A class has 32 boys and 45 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 32 and 45. Hence, GCF of 32 and 45 is 1.

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

GCF and LCM of two numbers can be related as GCF(32, 45) = ( 32 \* 45 ) / LCM(32, 45) = 1.

What is the GCF of 32 and 45?

GCF of 32 and 45 is 1.

Ram has 32 cans of Pepsi and 45 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 32 and 45. Hence GCF of 32 and 45 is 1. So the number of tables that can be arranged is 1.

Rubel is creating individual servings of starters for her birthday party. He has 32 pizzas and 45 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 32 and 45. Thus GCF of 32 and 45 is 1.

Ariel is making ready to eat meals to share with friends. She has 32 bottles of water and 45 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 32 and 45. So the GCF of 32 and 45 is 1.

Kamal is making identical balloon arrangements for a party. He has 32 maroon balloons, and 45 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 32 and 45. So the GCF of 32 and 45 is 1.

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 32 bus tickets and 45 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 32 and 45. Hence, GCF of 32 and 45 is 1.