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 (44, 99).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 44 and 99 is 11, where 11 is less than both 44 and 99.
- 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. 44 and 99 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 44 and also of 99.
- Every number is a factor of zero (0), since 44 x 0 = 0 and 99 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, 11, 22, 44 are exact divisors of 44 and 1, 3, 9, 11, 33, 99 are exact divisors of 99.
- Factors of 44 are 1, 2, 4, 11, 22, 44. Each factor divides 44 without leaving a remainder.
Simlarly, factors of 99 are 1, 3, 9, 11, 33, 99. Each factor divides 99 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 11, 22, 44 are all less than or equal to 44 and 1, 3, 9, 11, 33, 99 are all less than or equal to 99.
Steps to find Factors of 44 and 99
- Step 1. Find all the numbers that would divide 44 and 99 without leaving any remainder. Starting with the number 1 upto 22 (half of 44) and 1 upto 49 (half of 99). The number 1 and the number itself are always factors of the given number.
44 ÷ 1 : Remainder = 0
99 ÷ 1 : Remainder = 0
44 ÷ 2 : Remainder = 0
99 ÷ 3 : Remainder = 0
44 ÷ 4 : Remainder = 0
99 ÷ 9 : Remainder = 0
44 ÷ 11 : Remainder = 0
99 ÷ 11 : Remainder = 0
44 ÷ 22 : Remainder = 0
99 ÷ 33 : Remainder = 0
44 ÷ 44 : Remainder = 0
99 ÷ 99 : Remainder = 0
Hence, Factors of
44 are 1, 2, 4, 11, 22, and 44
And, Factors of
99 are 1, 3, 9, 11, 33, and 99
Examples of GCF
Sammy baked 44 chocolate cookies and 99 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 44 and 99.
GCF of 44 and 99 is 11.
A class has 44 boys and 99 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 44 and 99. Hence, GCF of 44 and 99 is 11.
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.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(44, 99) = ( 44 * 99 ) / LCM(44, 99) = 11.
What is the GCF of 44 and 99?GCF of 44 and 99 is 11.
Ariel is making ready to eat meals to share with friends. She has 44 bottles of water and 99 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 44 and 99. So the GCF of 44 and 99 is 11.
Mary has 44 blue buttons and 99 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 44 and 99. Hence, the GCF of 44 and 99 or the greatest arrangement is 11.
Kamal is making identical balloon arrangements for a party. He has 44 maroon balloons, and 99 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 44 and 99. So the GCF of 44 and 99 is 11.
Kunal is making baskets full of nuts and dried fruits. He has 44 bags of nuts and 99 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 44 and 99. So the GCF of 44 and 99 is 11.
A class has 44 boys and 99 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 44 and 99. Hence, GCF of 44 and 99 is 11.