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 (3125, 1300).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 3125 and 1300 is 25, where 25 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, 25, 125, 625, 3125 are exact divisors of 3125 and 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300 are exact divisors of 1300.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 3125 and 1300 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 3125 and also of 1300.
Steps to find Factors of 3125 and 1300
- Step 1. Find all the numbers that would divide 3125 and 1300 without leaving any remainder. Starting with the number 1 upto 1562 (half of 3125) and 1 upto 650 (half of 1300). The number 1 and the number itself are always factors of the given number.
3125 ÷ 1 : Remainder = 0
1300 ÷ 1 : Remainder = 0
3125 ÷ 5 : Remainder = 0
1300 ÷ 2 : Remainder = 0
3125 ÷ 25 : Remainder = 0
1300 ÷ 4 : Remainder = 0
3125 ÷ 125 : Remainder = 0
1300 ÷ 5 : Remainder = 0
3125 ÷ 625 : Remainder = 0
1300 ÷ 10 : Remainder = 0
3125 ÷ 3125 : Remainder = 0
1300 ÷ 13 : Remainder = 0
1300 ÷ 20 : Remainder = 0
1300 ÷ 25 : Remainder = 0
1300 ÷ 26 : Remainder = 0
1300 ÷ 50 : Remainder = 0
1300 ÷ 52 : Remainder = 0
1300 ÷ 65 : Remainder = 0
1300 ÷ 100 : Remainder = 0
1300 ÷ 130 : Remainder = 0
1300 ÷ 260 : Remainder = 0
1300 ÷ 325 : Remainder = 0
1300 ÷ 650 : Remainder = 0
1300 ÷ 1300 : Remainder = 0
Hence, Factors of
3125 are 1, 5, 25, 125, 625, and 3125
And, Factors of
1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, and 1300
Examples of GCF
A class has 3125 boys and 1300 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 3125 and 1300. Hence, GCF of 3125 and 1300 is 25.
What is the difference between GCF and LCM?Major and simple difference betwen GCF and LCM is that GCF gives you the greatest common factor while LCM finds out the least common factor possible for the given numbers.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(3125, 1300) = ( 3125 * 1300 ) / LCM(3125, 1300) = 25.
What is the GCF of 3125 and 1300?GCF of 3125 and 1300 is 25.
Ram has 3125 cans of Pepsi and 1300 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 3125 and 1300. Hence GCF of 3125 and 1300 is 25. So the number of tables that can be arranged is 25.
Rubel is creating individual servings of starters for her birthday party. He has 3125 pizzas and 1300 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 3125 and 1300. Thus GCF of 3125 and 1300 is 25.
Ariel is making ready to eat meals to share with friends. She has 3125 bottles of water and 1300 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 3125 and 1300. So the GCF of 3125 and 1300 is 25.
Mary has 3125 blue buttons and 1300 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 3125 and 1300. Hence, the GCF of 3125 and 1300 or the greatest arrangement is 25.
Kunal is making baskets full of nuts and dried fruits. He has 3125 bags of nuts and 1300 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 3125 and 1300. So the GCF of 3125 and 1300 is 25.