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, 560).
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 560 is 80, where 80 is less than both 320 and 560.
- 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 560 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 320 and also of 560.
- Every number is a factor of zero (0), since 320 x 0 = 0 and 560 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, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 are exact divisors of 560.
- 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 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560. Each factor divides 560 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, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 are all less than or equal to 560.
Steps to find Factors of 320 and 560
- Step 1. Find all the numbers that would divide 320 and 560 without leaving any remainder. Starting with the number 1 upto 160 (half of 320) and 1 upto 280 (half of 560). The number 1 and the number itself are always factors of the given number.
320 ÷ 1 : Remainder = 0
560 ÷ 1 : Remainder = 0
320 ÷ 2 : Remainder = 0
560 ÷ 2 : Remainder = 0
320 ÷ 4 : Remainder = 0
560 ÷ 4 : Remainder = 0
320 ÷ 5 : Remainder = 0
560 ÷ 5 : Remainder = 0
320 ÷ 8 : Remainder = 0
560 ÷ 7 : Remainder = 0
320 ÷ 10 : Remainder = 0
560 ÷ 8 : Remainder = 0
320 ÷ 16 : Remainder = 0
560 ÷ 10 : Remainder = 0
320 ÷ 20 : Remainder = 0
560 ÷ 14 : Remainder = 0
320 ÷ 32 : Remainder = 0
560 ÷ 16 : Remainder = 0
320 ÷ 40 : Remainder = 0
560 ÷ 20 : Remainder = 0
320 ÷ 64 : Remainder = 0
560 ÷ 28 : Remainder = 0
320 ÷ 80 : Remainder = 0
560 ÷ 35 : Remainder = 0
320 ÷ 160 : Remainder = 0
560 ÷ 40 : Remainder = 0
320 ÷ 320 : Remainder = 0
560 ÷ 56 : Remainder = 0
560 ÷ 112 : Remainder = 0
560 ÷ 140 : Remainder = 0
560 ÷ 280 : Remainder = 0
560 ÷ 560 : 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
560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, and 560
Examples of GCF
Sammy baked 320 chocolate cookies and 560 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 560.
GCF of 320 and 560 is 80.
A class has 320 boys and 560 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 560. Hence, GCF of 320 and 560 is 80.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(320, 560) = ( 320 * 560 ) / LCM(320, 560) = 80.
What is the GCF of 320 and 560?GCF of 320 and 560 is 80.
Ram has 320 cans of Pepsi and 560 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 560. Hence GCF of 320 and 560 is 80. So the number of tables that can be arranged is 80.
Rubel is creating individual servings of starters for her birthday party. He has 320 pizzas and 560 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 560. Thus GCF of 320 and 560 is 80.
Ariel is making ready to eat meals to share with friends. She has 320 bottles of water and 560 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 560. So the GCF of 320 and 560 is 80.
Kamal is making identical balloon arrangements for a party. He has 320 maroon balloons, and 560 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 560. So the GCF of 320 and 560 is 80.
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 560 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 560. Hence, GCF of 320 and 560 is 80.