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 (60, 75).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 60 and 75 is 15, where 15 is less than both 60 and 75.
- GCF of two consecutive numbers is always 1.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- 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
- Each number is a factor of itself. Eg. 60 and 75 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 60 and also of 75.
- Every number is a factor of zero (0), since 60 x 0 = 0 and 75 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, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 are exact divisors of 60 and 1, 3, 5, 15, 25, 75 are exact divisors of 75.
- Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Each factor divides 60 without leaving a remainder.
Simlarly, factors of 75 are 1, 3, 5, 15, 25, 75. Each factor divides 75 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 are all less than or equal to 60 and 1, 3, 5, 15, 25, 75 are all less than or equal to 75.
Steps to find Factors of 60 and 75
- Step 1. Find all the numbers that would divide 60 and 75 without leaving any remainder. Starting with the number 1 upto 30 (half of 60) and 1 upto 37 (half of 75). The number 1 and the number itself are always factors of the given number.
60 ÷ 1 : Remainder = 0
75 ÷ 1 : Remainder = 0
60 ÷ 2 : Remainder = 0
75 ÷ 3 : Remainder = 0
60 ÷ 3 : Remainder = 0
75 ÷ 5 : Remainder = 0
60 ÷ 4 : Remainder = 0
75 ÷ 15 : Remainder = 0
60 ÷ 5 : Remainder = 0
75 ÷ 25 : Remainder = 0
60 ÷ 6 : Remainder = 0
75 ÷ 75 : Remainder = 0
Hence, Factors of
60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
And, Factors of
75 are 1, 3, 5, 15, 25, and 75
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(60, 75) = ( 60 * 75 ) / LCM(60, 75) = 15.
What is the GCF of 60 and 75?GCF of 60 and 75 is 15.
Ram has 60 cans of Pepsi and 75 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 60 and 75. Hence GCF of 60 and 75 is 15. So the number of tables that can be arranged is 15.
Rubel is creating individual servings of starters for her birthday party. He has 60 pizzas and 75 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 60 and 75. Thus GCF of 60 and 75 is 15.
Ariel is making ready to eat meals to share with friends. She has 60 bottles of water and 75 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 60 and 75. So the GCF of 60 and 75 is 15.
Mary has 60 blue buttons and 75 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 60 and 75. Hence, the GCF of 60 and 75 or the greatest arrangement is 15.
Kamal is making identical balloon arrangements for a party. He has 60 maroon balloons, and 75 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 60 and 75. So the GCF of 60 and 75 is 15.
Kunal is making baskets full of nuts and dried fruits. He has 60 bags of nuts and 75 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 60 and 75. So the GCF of 60 and 75 is 15.
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 60 bus tickets and 75 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 60 and 75. Hence, GCF of 60 and 75 is 15.