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 (24, 1000).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 24 and 1000 is 8, where 8 is less than both 24 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. 24 and 1000 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 24 and also of 1000.
- Every number is a factor of zero (0), since 24 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, 3, 4, 6, 8, 12, 24 are exact divisors of 24 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are exact divisors of 1000.
- Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Each factor divides 24 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, 3, 4, 6, 8, 12, 24 are all less than or equal to 24 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 24 and 1000
- Step 1. Find all the numbers that would divide 24 and 1000 without leaving any remainder. Starting with the number 1 upto 12 (half of 24) and 1 upto 500 (half of 1000). The number 1 and the number itself are always factors of the given number.
24 ÷ 1 : Remainder = 0
1000 ÷ 1 : Remainder = 0
24 ÷ 2 : Remainder = 0
1000 ÷ 2 : Remainder = 0
24 ÷ 3 : Remainder = 0
1000 ÷ 4 : Remainder = 0
24 ÷ 4 : Remainder = 0
1000 ÷ 5 : Remainder = 0
24 ÷ 6 : Remainder = 0
1000 ÷ 8 : Remainder = 0
24 ÷ 8 : Remainder = 0
1000 ÷ 10 : Remainder = 0
24 ÷ 12 : Remainder = 0
1000 ÷ 20 : Remainder = 0
24 ÷ 24 : 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
24 are 1, 2, 3, 4, 6, 8, 12, and 24
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
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(24, 1000) = ( 24 * 1000 ) / LCM(24, 1000) = 8.
What is the GCF of 24 and 1000?GCF of 24 and 1000 is 8.
Ram has 24 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 24 and 1000. Hence GCF of 24 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 24 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 24 and 1000. Thus GCF of 24 and 1000 is 8.
Ariel is making ready to eat meals to share with friends. She has 24 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 24 and 1000. So the GCF of 24 and 1000 is 8.
Mary has 24 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 24 and 1000. Hence, the GCF of 24 and 1000 or the greatest arrangement is 8.
Kamal is making identical balloon arrangements for a party. He has 24 maroon balloons, and 1000 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 24 and 1000. So the GCF of 24 and 1000 is 8.
Kunal is making baskets full of nuts and dried fruits. He has 24 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 24 and 1000. So the GCF of 24 and 1000 is 8.
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 24 bus tickets and 1000 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 24 and 1000. Hence, GCF of 24 and 1000 is 8.