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 (320, 800).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 320 and 800 is 160, where 160 is less than both 320 and 800.
- 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.
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
- Each number is a factor of itself. Eg. 320 and 800 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 320 and also of 800.
- Every number is a factor of zero (0), since 320 x 0 = 0 and 800 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, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320 are exact divisors of 320 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800 are exact divisors of 800.
- Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. Each factor divides 320 without leaving a remainder.
Simlarly, factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800. Each factor divides 800 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320 are all less than or equal to 320 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800 are all less than or equal to 800.
Steps to find Factors of 320 and 800
- Step 1. Find all the numbers that would divide 320 and 800 without leaving any remainder. Starting with the number 1 upto 160 (half of 320) and 1 upto 400 (half of 800). The number 1 and the number itself are always factors of the given number.
320 ÷ 1 : Remainder = 0
800 ÷ 1 : Remainder = 0
320 ÷ 2 : Remainder = 0
800 ÷ 2 : Remainder = 0
320 ÷ 4 : Remainder = 0
800 ÷ 4 : Remainder = 0
320 ÷ 5 : Remainder = 0
800 ÷ 5 : Remainder = 0
320 ÷ 8 : Remainder = 0
800 ÷ 8 : Remainder = 0
320 ÷ 10 : Remainder = 0
800 ÷ 10 : Remainder = 0
320 ÷ 16 : Remainder = 0
800 ÷ 16 : Remainder = 0
320 ÷ 20 : Remainder = 0
800 ÷ 20 : Remainder = 0
320 ÷ 32 : Remainder = 0
800 ÷ 25 : Remainder = 0
320 ÷ 40 : Remainder = 0
800 ÷ 32 : Remainder = 0
320 ÷ 64 : Remainder = 0
800 ÷ 40 : Remainder = 0
320 ÷ 80 : Remainder = 0
800 ÷ 50 : Remainder = 0
320 ÷ 160 : Remainder = 0
800 ÷ 80 : Remainder = 0
320 ÷ 320 : Remainder = 0
800 ÷ 100 : Remainder = 0
800 ÷ 160 : Remainder = 0
800 ÷ 200 : Remainder = 0
800 ÷ 400 : Remainder = 0
800 ÷ 800 : Remainder = 0
Hence, Factors of
320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320
And, Factors of
800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800
Examples of GCF
Sammy baked 320 chocolate cookies and 800 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 320 and 800.
GCF of 320 and 800 is 160.
A class has 320 boys and 800 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 320 and 800. Hence, GCF of 320 and 800 is 160.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(320, 800) = ( 320 * 800 ) / LCM(320, 800) = 160.
What is the GCF of 320 and 800?GCF of 320 and 800 is 160.
Ram has 320 cans of Pepsi and 800 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 320 and 800. Hence GCF of 320 and 800 is 160. So the number of tables that can be arranged is 160.
Rubel is creating individual servings of starters for her birthday party. He has 320 pizzas and 800 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 320 and 800. Thus GCF of 320 and 800 is 160.
Ariel is making ready to eat meals to share with friends. She has 320 bottles of water and 800 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 320 and 800. So the GCF of 320 and 800 is 160.
Kamal is making identical balloon arrangements for a party. He has 320 maroon balloons, and 800 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 320 and 800. So the GCF of 320 and 800 is 160.
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 320 bus tickets and 800 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 320 and 800. Hence, GCF of 320 and 800 is 160.