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 (1089, 1386).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 1089 and 1386 is 99, where 99 is less than both the numbers.
- If the given numbers are consecutive than GCF is always 1.
- Product of two numbers is always equal to the product of their GCF and LCM.
- 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
- Every factor of a number is an exact divisor of that number, example 1, 3, 9, 11, 33, 99, 121, 363, 1089 are exact divisors of 1089 and 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 63, 66, 77, 99, 126, 154, 198, 231, 462, 693, 1386 are exact divisors of 1386.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 1089 and 1386 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1089 and also of 1386.
Steps to find Factors of 1089 and 1386
- Step 1. Find all the numbers that would divide 1089 and 1386 without leaving any remainder. Starting with the number 1 upto 544 (half of 1089) and 1 upto 693 (half of 1386). The number 1 and the number itself are always factors of the given number.
1089 ÷ 1 : Remainder = 0
1386 ÷ 1 : Remainder = 0
1089 ÷ 3 : Remainder = 0
1386 ÷ 2 : Remainder = 0
1089 ÷ 9 : Remainder = 0
1386 ÷ 3 : Remainder = 0
1089 ÷ 11 : Remainder = 0
1386 ÷ 6 : Remainder = 0
1089 ÷ 33 : Remainder = 0
1386 ÷ 7 : Remainder = 0
1089 ÷ 99 : Remainder = 0
1386 ÷ 9 : Remainder = 0
1089 ÷ 121 : Remainder = 0
1386 ÷ 11 : Remainder = 0
1089 ÷ 363 : Remainder = 0
1386 ÷ 14 : Remainder = 0
1089 ÷ 1089 : Remainder = 0
1386 ÷ 18 : Remainder = 0
1386 ÷ 21 : Remainder = 0
1386 ÷ 22 : Remainder = 0
1386 ÷ 33 : Remainder = 0
1386 ÷ 42 : Remainder = 0
1386 ÷ 63 : Remainder = 0
1386 ÷ 66 : Remainder = 0
1386 ÷ 77 : Remainder = 0
1386 ÷ 99 : Remainder = 0
1386 ÷ 126 : Remainder = 0
1386 ÷ 154 : Remainder = 0
1386 ÷ 198 : Remainder = 0
1386 ÷ 231 : Remainder = 0
1386 ÷ 462 : Remainder = 0
1386 ÷ 693 : Remainder = 0
1386 ÷ 1386 : Remainder = 0
Hence, Factors of
1089 are 1, 3, 9, 11, 33, 99, 121, 363, and 1089
And, Factors of
1386 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 63, 66, 77, 99, 126, 154, 198, 231, 462, 693, and 1386
Examples of GCF
Sammy baked 1089 chocolate cookies and 1386 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 1089 and 1386.
GCF of 1089 and 1386 is 99.
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(1089, 1386) = ( 1089 * 1386 ) / LCM(1089, 1386) = 99.
What is the GCF of 1089 and 1386?GCF of 1089 and 1386 is 99.
Ram has 1089 cans of Pepsi and 1386 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 1089 and 1386. Hence GCF of 1089 and 1386 is 99. So the number of tables that can be arranged is 99.
Rubel is creating individual servings of starters for her birthday party. He has 1089 pizzas and 1386 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 1089 and 1386. Thus GCF of 1089 and 1386 is 99.
Ariel is making ready to eat meals to share with friends. She has 1089 bottles of water and 1386 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 1089 and 1386. So the GCF of 1089 and 1386 is 99.
Mary has 1089 blue buttons and 1386 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 1089 and 1386. Hence, the GCF of 1089 and 1386 or the greatest arrangement is 99.
Kamal is making identical balloon arrangements for a party. He has 1089 maroon balloons, and 1386 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 1089 and 1386. So the GCF of 1089 and 1386 is 99.