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 (105, 210).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 105 and 210 is 105, where 105 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, 3, 5, 7, 15, 21, 35, 105 are exact divisors of 105 and 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 are exact divisors of 210.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 105 and 210 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 105 and also of 210.
Steps to find Factors of 105 and 210
- Step 1. Find all the numbers that would divide 105 and 210 without leaving any remainder. Starting with the number 1 upto 52 (half of 105) and 1 upto 105 (half of 210). The number 1 and the number itself are always factors of the given number.
105 ÷ 1 : Remainder = 0
210 ÷ 1 : Remainder = 0
105 ÷ 3 : Remainder = 0
210 ÷ 2 : Remainder = 0
105 ÷ 5 : Remainder = 0
210 ÷ 3 : Remainder = 0
105 ÷ 7 : Remainder = 0
210 ÷ 5 : Remainder = 0
105 ÷ 15 : Remainder = 0
210 ÷ 6 : Remainder = 0
105 ÷ 21 : Remainder = 0
210 ÷ 7 : Remainder = 0
105 ÷ 35 : Remainder = 0
210 ÷ 10 : Remainder = 0
105 ÷ 105 : Remainder = 0
210 ÷ 14 : Remainder = 0
210 ÷ 105 : Remainder = 0
210 ÷ 210 : Remainder = 0
Hence, Factors of
105 are 1, 3, 5, 7, 15, 21, 35, and 105
And, Factors of
210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210
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(105, 210) = ( 105 * 210 ) / LCM(105, 210) = 105.
What is the GCF of 105 and 210?GCF of 105 and 210 is 105.
Ram has 105 cans of Pepsi and 210 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 105 and 210. Hence GCF of 105 and 210 is 105. So the number of tables that can be arranged is 105.
Rubel is creating individual servings of starters for her birthday party. He has 105 pizzas and 210 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 105 and 210. Thus GCF of 105 and 210 is 105.
Ariel is making ready to eat meals to share with friends. She has 105 bottles of water and 210 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 105 and 210. So the GCF of 105 and 210 is 105.
Mary has 105 blue buttons and 210 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 105 and 210. Hence, the GCF of 105 and 210 or the greatest arrangement is 105.
Kamal is making identical balloon arrangements for a party. He has 105 maroon balloons, and 210 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 105 and 210. So the GCF of 105 and 210 is 105.
Kunal is making baskets full of nuts and dried fruits. He has 105 bags of nuts and 210 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 105 and 210. So the GCF of 105 and 210 is 105.
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 105 bus tickets and 210 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 105 and 210. Hence, GCF of 105 and 210 is 105.