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 (315, 735).
Properties of GCF
- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
- GCF of two consecutive numbers is always 1.
- Given two numbers 315 and 735, such that GCF is 105 where 105 will always be less than 315 and 735.
- Product of two numbers is always equal to the product of their GCF and LCM.
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 number is a factor of zero (0), since 315 x 0 = 0 and 735 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, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315 are exact divisors of 315 and 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735 are exact divisors of 735.
- Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Each factor divides 315 without leaving a remainder.
Simlarly, factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. Each factor divides 735 without leaving a remainder.
Steps to find Factors of 315 and 735
- Step 1. Find all the numbers that would divide 315 and 735 without leaving any remainder. Starting with the number 1 upto 157 (half of 315) and 1 upto 367 (half of 735). The number 1 and the number itself are always factors of the given number.
315 ÷ 1 : Remainder = 0
735 ÷ 1 : Remainder = 0
315 ÷ 3 : Remainder = 0
735 ÷ 3 : Remainder = 0
315 ÷ 5 : Remainder = 0
735 ÷ 5 : Remainder = 0
315 ÷ 7 : Remainder = 0
735 ÷ 7 : Remainder = 0
315 ÷ 9 : Remainder = 0
735 ÷ 15 : Remainder = 0
315 ÷ 15 : Remainder = 0
735 ÷ 21 : Remainder = 0
315 ÷ 21 : Remainder = 0
735 ÷ 35 : Remainder = 0
315 ÷ 35 : Remainder = 0
735 ÷ 49 : Remainder = 0
315 ÷ 45 : Remainder = 0
735 ÷ 105 : Remainder = 0
315 ÷ 63 : Remainder = 0
735 ÷ 147 : Remainder = 0
315 ÷ 105 : Remainder = 0
735 ÷ 245 : Remainder = 0
315 ÷ 315 : Remainder = 0
735 ÷ 735 : Remainder = 0
Hence, Factors of
315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315
And, Factors of
735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735
Examples of GCF
Sammy baked 315 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 315 and 735.
GCF of 315 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.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(315, 735) = ( 315 * 735 ) / LCM(315, 735) = 105.
What is the GCF of 315 and 735?GCF of 315 and 735 is 105.
Ram has 315 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 315 and 735. Hence GCF of 315 and 735 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 315 pizzas and 735 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 315 and 735. Thus GCF of 315 and 735 is 105.
Ariel is making ready to eat meals to share with friends. She has 315 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 315 and 735. So the GCF of 315 and 735 is 105.
Mary has 315 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 315 and 735. Hence, the GCF of 315 and 735 or the greatest arrangement is 105.
Kamal is making identical balloon arrangements for a party. He has 315 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 315 and 735. So the GCF of 315 and 735 is 105.