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 (210, 735).
Properties of GCF
- Given two numbers 210 and 735, such that GCF is 105 where 105 will always be less than 210 and 735.
- 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. 210 and 735 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, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210 are exact divisors of 210 and 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735 are exact divisors of 735.
- 1 is a factor of every number. Eg. 1 is a factor of 210 and also of 735.
- Every number is a factor of zero (0), since 210 x 0 = 0 and 735 x 0 = 0.
Steps to find Factors of 210 and 735
- Step 1. Find all the numbers that would divide 210 and 735 without leaving any remainder. Starting with the number 1 upto 105 (half of 210) and 1 upto 367 (half of 735). The number 1 and the number itself are always factors of the given number.
210 ÷ 1 : Remainder = 0
735 ÷ 1 : Remainder = 0
210 ÷ 2 : Remainder = 0
735 ÷ 3 : Remainder = 0
210 ÷ 3 : Remainder = 0
735 ÷ 5 : Remainder = 0
210 ÷ 5 : Remainder = 0
735 ÷ 7 : Remainder = 0
210 ÷ 6 : Remainder = 0
735 ÷ 15 : Remainder = 0
210 ÷ 7 : Remainder = 0
735 ÷ 21 : Remainder = 0
210 ÷ 10 : Remainder = 0
735 ÷ 35 : Remainder = 0
210 ÷ 14 : Remainder = 0
735 ÷ 49 : Remainder = 0
210 ÷ 15 : Remainder = 0
735 ÷ 105 : Remainder = 0
210 ÷ 21 : Remainder = 0
735 ÷ 147 : Remainder = 0
210 ÷ 30 : Remainder = 0
735 ÷ 245 : Remainder = 0
210 ÷ 35 : Remainder = 0
735 ÷ 735 : Remainder = 0
210 ÷ 105 : Remainder = 0
210 ÷ 210 : Remainder = 0
Hence, Factors of
210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210
And, Factors of
735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735
Examples of GCF
Sammy baked 210 chocolate cookies and 735 fruit and nut cookies to package in plastic containers for her friends at college. She wants to divide the cookies into identical boxes so that each box has the same number of each kind of cookies. She wishes that each box should have greatest number of cookies possible, how many plastic boxes does she need?Since Sammy wants to pack greatest number of cookies possible. So for calculating total number of boxes required we need to calculate the GCF of 210 and 735.
GCF of 210 and 735 is 105.
A class has 210 boys and 735 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 210 and 735. Hence, GCF of 210 and 735 is 105.
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.
Ram has 210 cans of Pepsi and 735 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 210 and 735. Hence GCF of 210 and 735 is 105. So the number of tables that can be arranged is 105.
Ariel is making ready to eat meals to share with friends. She has 210 bottles of water and 735 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 210 and 735. So the GCF of 210 and 735 is 105.
Mary has 210 blue buttons and 735 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 210 and 735. Hence, the GCF of 210 and 735 or the greatest arrangement is 105.
Kamal is making identical balloon arrangements for a party. He has 210 maroon balloons, and 735 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 210 and 735. So the GCF of 210 and 735 is 105.
Kunal is making baskets full of nuts and dried fruits. He has 210 bags of nuts and 735 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 210 and 735. So the GCF of 210 and 735 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 210 bus tickets and 735 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 210 and 735. Hence, GCF of 210 and 735 is 105.