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 (64, 84).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 64 and 84 is 4, where 4 is less than both 64 and 84.
- 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.
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
- Each number is a factor of itself. Eg. 64 and 84 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 64 and also of 84.
- Every number is a factor of zero (0), since 64 x 0 = 0 and 84 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, 4, 8, 16, 32, 64 are exact divisors of 64 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are exact divisors of 84.
- Factors of 64 are 1, 2, 4, 8, 16, 32, 64. Each factor divides 64 without leaving a remainder.
Simlarly, factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Each factor divides 84 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64 are all less than or equal to 64 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are all less than or equal to 84.
Steps to find Factors of 64 and 84
- Step 1. Find all the numbers that would divide 64 and 84 without leaving any remainder. Starting with the number 1 upto 32 (half of 64) and 1 upto 42 (half of 84). The number 1 and the number itself are always factors of the given number.
64 ÷ 1 : Remainder = 0
84 ÷ 1 : Remainder = 0
64 ÷ 2 : Remainder = 0
84 ÷ 2 : Remainder = 0
64 ÷ 4 : Remainder = 0
84 ÷ 3 : Remainder = 0
64 ÷ 8 : Remainder = 0
84 ÷ 4 : Remainder = 0
64 ÷ 16 : Remainder = 0
84 ÷ 6 : Remainder = 0
64 ÷ 32 : Remainder = 0
84 ÷ 7 : Remainder = 0
64 ÷ 64 : Remainder = 0
84 ÷ 12 : Remainder = 0
Hence, Factors of
64 are 1, 2, 4, 8, 16, 32, and 64
And, Factors of
84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84
Examples of GCF
Sammy baked 64 chocolate cookies and 84 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 64 and 84.
GCF of 64 and 84 is 4.
A class has 64 boys and 84 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 64 and 84. Hence, GCF of 64 and 84 is 4.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(64, 84) = ( 64 * 84 ) / LCM(64, 84) = 4.
What is the GCF of 64 and 84?GCF of 64 and 84 is 4.
Ram has 64 cans of Pepsi and 84 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 64 and 84. Hence GCF of 64 and 84 is 4. So the number of tables that can be arranged is 4.
Mary has 64 blue buttons and 84 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 64 and 84. Hence, the GCF of 64 and 84 or the greatest arrangement is 4.
Kamal is making identical balloon arrangements for a party. He has 64 maroon balloons, and 84 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 64 and 84. So the GCF of 64 and 84 is 4.
Kunal is making baskets full of nuts and dried fruits. He has 64 bags of nuts and 84 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 64 and 84. So the GCF of 64 and 84 is 4.
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 64 bus tickets and 84 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 64 and 84. Hence, GCF of 64 and 84 is 4.