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 (15, 78).
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 15 and 78, such that GCF is 3 where 3 will always be less than 15 and 78.
- 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 15 x 0 = 0 and 78 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, 15 are exact divisors of 15 and 1, 2, 3, 6, 13, 26, 39, 78 are exact divisors of 78.
- Factors of 15 are 1, 3, 5, 15. Each factor divides 15 without leaving a remainder.
Simlarly, factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. Each factor divides 78 without leaving a remainder.
Steps to find Factors of 15 and 78
- Step 1. Find all the numbers that would divide 15 and 78 without leaving any remainder. Starting with the number 1 upto 7 (half of 15) and 1 upto 39 (half of 78). The number 1 and the number itself are always factors of the given number.
15 ÷ 1 : Remainder = 0
78 ÷ 1 : Remainder = 0
15 ÷ 3 : Remainder = 0
78 ÷ 2 : Remainder = 0
15 ÷ 5 : Remainder = 0
78 ÷ 3 : Remainder = 0
15 ÷ 15 : Remainder = 0
78 ÷ 6 : Remainder = 0
Hence, Factors of
15 are 1, 3, 5, and 15
And, Factors of
78 are 1, 2, 3, 6, 13, 26, 39, and 78
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(15, 78) = ( 15 * 78 ) / LCM(15, 78) = 3.
What is the GCF of 15 and 78?
GCF of 15 and 78 is 3.
Ram has 15 cans of Pepsi and 78 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 15 and 78. Hence GCF of 15 and 78 is 3. So the number of tables that can be arranged is 3.
Rubel is creating individual servings of starters for her birthday party. He has 15 pizzas and 78 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 15 and 78. Thus GCF of 15 and 78 is 3.
Ariel is making ready to eat meals to share with friends. She has 15 bottles of water and 78 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 15 and 78. So the GCF of 15 and 78 is 3.
Mary has 15 blue buttons and 78 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 15 and 78. Hence, the GCF of 15 and 78 or the greatest arrangement is 3.
Kamal is making identical balloon arrangements for a party. He has 15 maroon balloons, and 78 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 15 and 78. So the GCF of 15 and 78 is 3.
Kunal is making baskets full of nuts and dried fruits. He has 15 bags of nuts and 78 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 15 and 78. So the GCF of 15 and 78 is 3.
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 15 bus tickets and 78 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 15 and 78. Hence, GCF of 15 and 78 is 3.