How do you explain GCF in mathematics?
GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (39, 90).
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 39 and 90, such that GCF is 3 where 3 will always be less than 39 and 90.
- Product of two numbers is always equal to the product of their GCF and LCM.
How can we define factors?
In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.
Properties of Factors
- Every number is a factor of zero (0), since 39 x 0 = 0 and 90 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, 13, 39 are exact divisors of 39 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 are exact divisors of 90.
- Factors of 39 are 1, 3, 13, 39. Each factor divides 39 without leaving a remainder.
Simlarly, factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Each factor divides 90 without leaving a remainder.
Steps to find Factors of 39 and 90
- Step 1. Find all the numbers that would divide 39 and 90 without leaving any remainder. Starting with the number 1 upto 19 (half of 39) and 1 upto 45 (half of 90). The number 1 and the number itself are always factors of the given number.
39 ÷ 1 : Remainder = 0
90 ÷ 1 : Remainder = 0
39 ÷ 3 : Remainder = 0
90 ÷ 2 : Remainder = 0
39 ÷ 13 : Remainder = 0
90 ÷ 3 : Remainder = 0
39 ÷ 39 : Remainder = 0
90 ÷ 5 : Remainder = 0
Hence, Factors of
39 are 1, 3, 13, and 39
And, Factors of
90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Examples of GCF
Sammy baked 39 chocolate cookies and 90 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 39 and 90.
GCF of 39 and 90 is 3.
A class has 39 boys and 90 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 39 and 90. Hence, GCF of 39 and 90 is 3.
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 39 cans of Pepsi and 90 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 39 and 90. Hence GCF of 39 and 90 is 3. So the number of tables that can be arranged is 3.
Ariel is making ready to eat meals to share with friends. She has 39 bottles of water and 90 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 39 and 90. So the GCF of 39 and 90 is 3.
Mary has 39 blue buttons and 90 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 39 and 90. Hence, the GCF of 39 and 90 or the greatest arrangement is 3.
Kamal is making identical balloon arrangements for a party. He has 39 maroon balloons, and 90 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 39 and 90. So the GCF of 39 and 90 is 3.
Kunal is making baskets full of nuts and dried fruits. He has 39 bags of nuts and 90 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 39 and 90. So the GCF of 39 and 90 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 39 bus tickets and 90 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 39 and 90. Hence, GCF of 39 and 90 is 3.