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 (150, 210).
Properties of GCF
- Given two numbers 150 and 210, such that GCF is 30 where 30 will always be less than 150 and 210.
- GCF of two numbers is always equal to 1 in case given numbers are consecutive.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.
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
- Each number is a factor of itself. Eg. 150 and 210 are factors of themselves respectively.
- 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, 5, 6, 10, 15, 25, 30, 50, 75, 150 are exact divisors of 150 and 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 are exact divisors of 210.
- 1 is a factor of every number. Eg. 1 is a factor of 150 and also of 210.
- Every number is a factor of zero (0), since 150 x 0 = 0 and 210 x 0 = 0.
Steps to find Factors of 150 and 210
- Step 1. Find all the numbers that would divide 150 and 210 without leaving any remainder. Starting with the number 1 upto 75 (half of 150) and 1 upto 105 (half of 210). The number 1 and the number itself are always factors of the given number.
150 ÷ 1 : Remainder = 0
210 ÷ 1 : Remainder = 0
150 ÷ 2 : Remainder = 0
210 ÷ 2 : Remainder = 0
150 ÷ 3 : Remainder = 0
210 ÷ 3 : Remainder = 0
150 ÷ 5 : Remainder = 0
210 ÷ 5 : Remainder = 0
150 ÷ 6 : Remainder = 0
210 ÷ 6 : Remainder = 0
150 ÷ 10 : Remainder = 0
210 ÷ 7 : Remainder = 0
150 ÷ 15 : Remainder = 0
210 ÷ 10 : Remainder = 0
150 ÷ 25 : Remainder = 0
210 ÷ 14 : Remainder = 0
150 ÷ 30 : Remainder = 0
210 ÷ 15 : Remainder = 0
150 ÷ 50 : Remainder = 0
210 ÷ 21 : Remainder = 0
150 ÷ 75 : Remainder = 0
210 ÷ 30 : Remainder = 0
150 ÷ 150 : Remainder = 0
210 ÷ 35 : Remainder = 0
210 ÷ 105 : Remainder = 0
210 ÷ 210 : Remainder = 0
Hence, Factors of
150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150
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(150, 210) = ( 150 * 210 ) / LCM(150, 210) = 30.
What is the GCF of 150 and 210?GCF of 150 and 210 is 30.
Ram has 150 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 150 and 210. Hence GCF of 150 and 210 is 30. So the number of tables that can be arranged is 30.
Rubel is creating individual servings of starters for her birthday party. He has 150 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 150 and 210. Thus GCF of 150 and 210 is 30.
Ariel is making ready to eat meals to share with friends. She has 150 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 150 and 210. So the GCF of 150 and 210 is 30.
Mary has 150 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 150 and 210. Hence, the GCF of 150 and 210 or the greatest arrangement is 30.
Kamal is making identical balloon arrangements for a party. He has 150 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 150 and 210. So the GCF of 150 and 210 is 30.
Kunal is making baskets full of nuts and dried fruits. He has 150 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 150 and 210. So the GCF of 150 and 210 is 30.
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 150 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 150 and 210. Hence, GCF of 150 and 210 is 30.