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 (344, 1000).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 344 and 1000 is 8, where 8 is less than both 344 and 1000.
- 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.
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
- Each number is a factor of itself. Eg. 344 and 1000 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 344 and also of 1000.
- Every number is a factor of zero (0), since 344 x 0 = 0 and 1000 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, 8, 43, 86, 172, 344 are exact divisors of 344 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are exact divisors of 1000.
- Factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344. Each factor divides 344 without leaving a remainder.
Simlarly, factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. Each factor divides 1000 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 43, 86, 172, 344 are all less than or equal to 344 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are all less than or equal to 1000.
Steps to find Factors of 344 and 1000
- Step 1. Find all the numbers that would divide 344 and 1000 without leaving any remainder. Starting with the number 1 upto 172 (half of 344) and 1 upto 500 (half of 1000). The number 1 and the number itself are always factors of the given number.
344 ÷ 1 : Remainder = 0
1000 ÷ 1 : Remainder = 0
344 ÷ 2 : Remainder = 0
1000 ÷ 2 : Remainder = 0
344 ÷ 4 : Remainder = 0
1000 ÷ 4 : Remainder = 0
344 ÷ 8 : Remainder = 0
1000 ÷ 5 : Remainder = 0
344 ÷ 43 : Remainder = 0
1000 ÷ 8 : Remainder = 0
344 ÷ 86 : Remainder = 0
1000 ÷ 10 : Remainder = 0
344 ÷ 172 : Remainder = 0
1000 ÷ 20 : Remainder = 0
344 ÷ 344 : Remainder = 0
1000 ÷ 25 : Remainder = 0
1000 ÷ 40 : Remainder = 0
1000 ÷ 50 : Remainder = 0
1000 ÷ 100 : Remainder = 0
1000 ÷ 125 : Remainder = 0
1000 ÷ 200 : Remainder = 0
1000 ÷ 250 : Remainder = 0
1000 ÷ 500 : Remainder = 0
1000 ÷ 1000 : Remainder = 0
Hence, Factors of
344 are 1, 2, 4, 8, 43, 86, 172, and 344
And, Factors of
1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000
Examples of GCF
A class has 344 boys and 1000 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 344 and 1000. Hence, GCF of 344 and 1000 is 8.
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(344, 1000) = ( 344 * 1000 ) / LCM(344, 1000) = 8.
What is the GCF of 344 and 1000?GCF of 344 and 1000 is 8.
Ram has 344 cans of Pepsi and 1000 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 344 and 1000. Hence GCF of 344 and 1000 is 8. So the number of tables that can be arranged is 8.
Rubel is creating individual servings of starters for her birthday party. He has 344 pizzas and 1000 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 344 and 1000. Thus GCF of 344 and 1000 is 8.
Ariel is making ready to eat meals to share with friends. She has 344 bottles of water and 1000 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 344 and 1000. So the GCF of 344 and 1000 is 8.
Mary has 344 blue buttons and 1000 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 344 and 1000. Hence, the GCF of 344 and 1000 or the greatest arrangement is 8.
Kunal is making baskets full of nuts and dried fruits. He has 344 bags of nuts and 1000 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 344 and 1000. So the GCF of 344 and 1000 is 8.