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 (325, 650).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 325 and 650 is 325, where 325 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.
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
- Every factor of a number is an exact divisor of that number, example 1, 5, 13, 25, 65, 325 are exact divisors of 325 and 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 are exact divisors of 650.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 325 and 650 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 325 and also of 650.
Steps to find Factors of 325 and 650
- Step 1. Find all the numbers that would divide 325 and 650 without leaving any remainder. Starting with the number 1 upto 162 (half of 325) and 1 upto 325 (half of 650). The number 1 and the number itself are always factors of the given number.
325 ÷ 1 : Remainder = 0
650 ÷ 1 : Remainder = 0
325 ÷ 5 : Remainder = 0
650 ÷ 2 : Remainder = 0
325 ÷ 13 : Remainder = 0
650 ÷ 5 : Remainder = 0
325 ÷ 25 : Remainder = 0
650 ÷ 10 : Remainder = 0
325 ÷ 65 : Remainder = 0
650 ÷ 13 : Remainder = 0
325 ÷ 325 : Remainder = 0
650 ÷ 25 : Remainder = 0
650 ÷ 130 : Remainder = 0
650 ÷ 325 : Remainder = 0
650 ÷ 650 : Remainder = 0
Hence, Factors of
325 are 1, 5, 13, 25, 65, and 325
And, Factors of
650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, and 650
Examples of GCF
Sammy baked 325 chocolate cookies and 650 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 325 and 650.
GCF of 325 and 650 is 325.
A class has 325 boys and 650 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 325 and 650. Hence, GCF of 325 and 650 is 325.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(325, 650) = ( 325 * 650 ) / LCM(325, 650) = 325.
What is the GCF of 325 and 650?GCF of 325 and 650 is 325.
Ram has 325 cans of Pepsi and 650 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 325 and 650. Hence GCF of 325 and 650 is 325. So the number of tables that can be arranged is 325.
Mary has 325 blue buttons and 650 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 325 and 650. Hence, the GCF of 325 and 650 or the greatest arrangement is 325.
Kamal is making identical balloon arrangements for a party. He has 325 maroon balloons, and 650 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 325 and 650. So the GCF of 325 and 650 is 325.
Kunal is making baskets full of nuts and dried fruits. He has 325 bags of nuts and 650 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 325 and 650. So the GCF of 325 and 650 is 325.
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 325 bus tickets and 650 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 325 and 650. Hence, GCF of 325 and 650 is 325.