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 (1369, 400).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 1369 and 400 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, 37, 1369 are exact divisors of 1369 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are exact divisors of 400.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 1369 and 400 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1369 and also of 400.
Steps to find Factors of 1369 and 400
- Step 1. Find all the numbers that would divide 1369 and 400 without leaving any remainder. Starting with the number 1 upto 684 (half of 1369) and 1 upto 200 (half of 400). The number 1 and the number itself are always factors of the given number.
1369 ÷ 1 : Remainder = 0
400 ÷ 1 : Remainder = 0
1369 ÷ 37 : Remainder = 0
400 ÷ 2 : Remainder = 0
1369 ÷ 1369 : Remainder = 0
400 ÷ 4 : Remainder = 0
400 ÷ 100 : Remainder = 0
400 ÷ 200 : Remainder = 0
400 ÷ 400 : Remainder = 0
Hence, Factors of
1369 are 1, 37, and 1369
And, Factors of
400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400
Examples of GCF
Sammy baked 1369 chocolate cookies and 400 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 1369 and 400.
GCF of 1369 and 400 is 1.
A class has 1369 boys and 400 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 1369 and 400. Hence, GCF of 1369 and 400 is 1.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(1369, 400) = ( 1369 * 400 ) / LCM(1369, 400) = 1.
What is the GCF of 1369 and 400?GCF of 1369 and 400 is 1.
Ram has 1369 cans of Pepsi and 400 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 1369 and 400. Hence GCF of 1369 and 400 is 1. So the number of tables that can be arranged is 1.
Mary has 1369 blue buttons and 400 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 1369 and 400. Hence, the GCF of 1369 and 400 or the greatest arrangement is 1.
Kamal is making identical balloon arrangements for a party. He has 1369 maroon balloons, and 400 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 1369 and 400. So the GCF of 1369 and 400 is 1.
Kunal is making baskets full of nuts and dried fruits. He has 1369 bags of nuts and 400 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?the greatest number of baskets that Kunal can make would be equal to GCF of 1369 and 400. So the GCF of 1369 and 400 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 1369 bus tickets and 400 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 1369 and 400. Hence, GCF of 1369 and 400 is 1.