How do you explain GCF in mathematics?
GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (329, 73000).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 329 and 73000 is 1, where 1 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.
How can we define factors?
In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.
Properties of Factors
- Every factor of a number is an exact divisor of that number, example 1, 7, 47, 329 are exact divisors of 329 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 73, 100, 125, 146, 200, 250, 292, 365, 500, 584, 730, 1000, 1460, 1825, 2920, 3650, 7300, 9125, 14600, 18250, 36500, 73000 are exact divisors of 73000.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 329 and 73000 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 329 and also of 73000.
Steps to find Factors of 329 and 73000
- Step 1. Find all the numbers that would divide 329 and 73000 without leaving any remainder. Starting with the number 1 upto 164 (half of 329) and 1 upto 36500 (half of 73000). The number 1 and the number itself are always factors of the given number.
329 ÷ 1 : Remainder = 0
73000 ÷ 1 : Remainder = 0
329 ÷ 7 : Remainder = 0
73000 ÷ 2 : Remainder = 0
329 ÷ 47 : Remainder = 0
73000 ÷ 4 : Remainder = 0
329 ÷ 329 : Remainder = 0
73000 ÷ 5 : Remainder = 0
73000 ÷ 8 : Remainder = 0
73000 ÷ 10 : Remainder = 0
73000 ÷ 20 : Remainder = 0
73000 ÷ 25 : Remainder = 0
73000 ÷ 40 : Remainder = 0
73000 ÷ 50 : Remainder = 0
73000 ÷ 73 : Remainder = 0
73000 ÷ 100 : Remainder = 0
73000 ÷ 125 : Remainder = 0
73000 ÷ 146 : Remainder = 0
73000 ÷ 200 : Remainder = 0
73000 ÷ 250 : Remainder = 0
73000 ÷ 292 : Remainder = 0
73000 ÷ 365 : Remainder = 0
73000 ÷ 500 : Remainder = 0
73000 ÷ 584 : Remainder = 0
73000 ÷ 730 : Remainder = 0
73000 ÷ 1000 : Remainder = 0
73000 ÷ 1460 : Remainder = 0
73000 ÷ 1825 : Remainder = 0
73000 ÷ 2920 : Remainder = 0
73000 ÷ 3650 : Remainder = 0
73000 ÷ 7300 : Remainder = 0
73000 ÷ 9125 : Remainder = 0
73000 ÷ 14600 : Remainder = 0
73000 ÷ 18250 : Remainder = 0
73000 ÷ 36500 : Remainder = 0
73000 ÷ 73000 : Remainder = 0
Hence, Factors of
329 are 1, 7, 47, and 329
And, Factors of
73000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 73, 100, 125, 146, 200, 250, 292, 365, 500, 584, 730, 1000, 1460, 1825, 2920, 3650, 7300, 9125, 14600, 18250, 36500, and 73000
Examples of GCF
Sammy baked 329 chocolate cookies and 73000 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 329 and 73000.
GCF of 329 and 73000 is 1.
A class has 329 boys and 73000 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 329 and 73000. Hence, GCF of 329 and 73000 is 1.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(329, 73000) = ( 329 * 73000 ) / LCM(329, 73000) = 1.
What is the GCF of 329 and 73000?GCF of 329 and 73000 is 1.
Ram has 329 cans of Pepsi and 73000 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 329 and 73000. Hence GCF of 329 and 73000 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 329 pizzas and 73000 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 329 and 73000. Thus GCF of 329 and 73000 is 1.
Ariel is making ready to eat meals to share with friends. She has 329 bottles of water and 73000 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 329 and 73000. So the GCF of 329 and 73000 is 1.
Kamal is making identical balloon arrangements for a party. He has 329 maroon balloons, and 73000 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 329 and 73000. So the GCF of 329 and 73000 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 329 bus tickets and 73000 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 329 and 73000. Hence, GCF of 329 and 73000 is 1.