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, 66).
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 66 is 22, where 22 is less than both 44 and 66.
- 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 66 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 44 and also of 66.
- Every number is a factor of zero (0), since 44 x 0 = 0 and 66 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, 2, 3, 6, 11, 22, 33, 66 are exact divisors of 66.
- Factors of 44 are 1, 2, 4, 11, 22, 44. Each factor divides 44 without leaving a remainder.
Simlarly, factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. Each factor divides 66 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, 2, 3, 6, 11, 22, 33, 66 are all less than or equal to 66.
Steps to find Factors of 44 and 66
- Step 1. Find all the numbers that would divide 44 and 66 without leaving any remainder. Starting with the number 1 upto 22 (half of 44) and 1 upto 33 (half of 66). The number 1 and the number itself are always factors of the given number.
44 ÷ 1 : Remainder = 0
66 ÷ 1 : Remainder = 0
44 ÷ 2 : Remainder = 0
66 ÷ 2 : Remainder = 0
44 ÷ 4 : Remainder = 0
66 ÷ 3 : Remainder = 0
44 ÷ 11 : Remainder = 0
66 ÷ 6 : Remainder = 0
44 ÷ 22 : Remainder = 0
66 ÷ 11 : Remainder = 0
44 ÷ 44 : Remainder = 0
66 ÷ 22 : Remainder = 0
Hence, Factors of
44 are 1, 2, 4, 11, 22, and 44
And, Factors of
66 are 1, 2, 3, 6, 11, 22, 33, and 66
Examples of GCF
Sammy baked 44 chocolate cookies and 66 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 66.
GCF of 44 and 66 is 22.
A class has 44 boys and 66 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 66. Hence, GCF of 44 and 66 is 22.
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, 66) = ( 44 * 66 ) / LCM(44, 66) = 22.
What is the GCF of 44 and 66?GCF of 44 and 66 is 22.
Ariel is making ready to eat meals to share with friends. She has 44 bottles of water and 66 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 66. So the GCF of 44 and 66 is 22.
Mary has 44 blue buttons and 66 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 66. Hence, the GCF of 44 and 66 or the greatest arrangement is 22.
Kamal is making identical balloon arrangements for a party. He has 44 maroon balloons, and 66 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 66. So the GCF of 44 and 66 is 22.
Kunal is making baskets full of nuts and dried fruits. He has 44 bags of nuts and 66 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 66. So the GCF of 44 and 66 is 22.
A class has 44 boys and 66 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 66. Hence, GCF of 44 and 66 is 22.