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 (50, 60).
Properties of GCF
- Given two numbers 50 and 60, such that GCF is 10 where 10 will always be less than 50 and 60.
- 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. 50 and 60 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, 5, 10, 25, 50 are exact divisors of 50 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 are exact divisors of 60.
- 1 is a factor of every number. Eg. 1 is a factor of 50 and also of 60.
- Every number is a factor of zero (0), since 50 x 0 = 0 and 60 x 0 = 0.
Steps to find Factors of 50 and 60
- Step 1. Find all the numbers that would divide 50 and 60 without leaving any remainder. Starting with the number 1 upto 25 (half of 50) and 1 upto 30 (half of 60). The number 1 and the number itself are always factors of the given number.
50 ÷ 1 : Remainder = 0
60 ÷ 1 : Remainder = 0
50 ÷ 2 : Remainder = 0
60 ÷ 2 : Remainder = 0
50 ÷ 5 : Remainder = 0
60 ÷ 3 : Remainder = 0
50 ÷ 10 : Remainder = 0
60 ÷ 4 : Remainder = 0
50 ÷ 25 : Remainder = 0
60 ÷ 5 : Remainder = 0
50 ÷ 50 : Remainder = 0
60 ÷ 6 : Remainder = 0
Hence, Factors of
50 are 1, 2, 5, 10, 25, and 50
And, Factors of
60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
Examples of GCF
Sammy baked 50 chocolate cookies and 60 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 50 and 60.
GCF of 50 and 60 is 10.
A class has 50 boys and 60 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 50 and 60. Hence, GCF of 50 and 60 is 10.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(50, 60) = ( 50 * 60 ) / LCM(50, 60) = 10.
What is the GCF of 50 and 60?GCF of 50 and 60 is 10.
Ram has 50 cans of Pepsi and 60 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 50 and 60. Hence GCF of 50 and 60 is 10. So the number of tables that can be arranged is 10.
Rubel is creating individual servings of starters for her birthday party. He has 50 pizzas and 60 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 50 and 60. Thus GCF of 50 and 60 is 10.
Ariel is making ready to eat meals to share with friends. She has 50 bottles of water and 60 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 50 and 60. So the GCF of 50 and 60 is 10.
Kamal is making identical balloon arrangements for a party. He has 50 maroon balloons, and 60 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 50 and 60. So the GCF of 50 and 60 is 10.
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 50 bus tickets and 60 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 50 and 60. Hence, GCF of 50 and 60 is 10.