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 (204, 342).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 204 and 342 is 6, where 6 is less than both 204 and 342.
- 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. 204 and 342 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 204 and also of 342.
- Every number is a factor of zero (0), since 204 x 0 = 0 and 342 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, 12, 17, 34, 51, 68, 102, 204 are exact divisors of 204 and 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342 are exact divisors of 342.
- Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. Each factor divides 204 without leaving a remainder.
Simlarly, factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342. Each factor divides 342 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204 are all less than or equal to 204 and 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342 are all less than or equal to 342.
Steps to find Factors of 204 and 342
- Step 1. Find all the numbers that would divide 204 and 342 without leaving any remainder. Starting with the number 1 upto 102 (half of 204) and 1 upto 171 (half of 342). The number 1 and the number itself are always factors of the given number.
204 ÷ 1 : Remainder = 0
342 ÷ 1 : Remainder = 0
204 ÷ 2 : Remainder = 0
342 ÷ 2 : Remainder = 0
204 ÷ 3 : Remainder = 0
342 ÷ 3 : Remainder = 0
204 ÷ 4 : Remainder = 0
342 ÷ 6 : Remainder = 0
204 ÷ 6 : Remainder = 0
342 ÷ 9 : Remainder = 0
204 ÷ 12 : Remainder = 0
342 ÷ 18 : Remainder = 0
204 ÷ 17 : Remainder = 0
342 ÷ 19 : Remainder = 0
204 ÷ 34 : Remainder = 0
342 ÷ 38 : Remainder = 0
204 ÷ 51 : Remainder = 0
342 ÷ 57 : Remainder = 0
204 ÷ 68 : Remainder = 0
342 ÷ 114 : Remainder = 0
204 ÷ 102 : Remainder = 0
342 ÷ 171 : Remainder = 0
204 ÷ 204 : Remainder = 0
342 ÷ 342 : Remainder = 0
Hence, Factors of
204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204
And, Factors of
342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, and 342
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(204, 342) = ( 204 * 342 ) / LCM(204, 342) = 6.
What is the GCF of 204 and 342?GCF of 204 and 342 is 6.
Ram has 204 cans of Pepsi and 342 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 204 and 342. Hence GCF of 204 and 342 is 6. So the number of tables that can be arranged is 6.
Rubel is creating individual servings of starters for her birthday party. He has 204 pizzas and 342 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 204 and 342. Thus GCF of 204 and 342 is 6.
Ariel is making ready to eat meals to share with friends. She has 204 bottles of water and 342 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 204 and 342. So the GCF of 204 and 342 is 6.
Mary has 204 blue buttons and 342 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 204 and 342. Hence, the GCF of 204 and 342 or the greatest arrangement is 6.
Kamal is making identical balloon arrangements for a party. He has 204 maroon balloons, and 342 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 204 and 342. So the GCF of 204 and 342 is 6.
Kunal is making baskets full of nuts and dried fruits. He has 204 bags of nuts and 342 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 204 and 342. So the GCF of 204 and 342 is 6.
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 204 bus tickets and 342 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 204 and 342. Hence, GCF of 204 and 342 is 6.