Definition of GCF
Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (45, 126).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 45 and 126 is 9, where 9 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.
What are factors?
In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.
Properties of Factors
- Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 45 are exact divisors of 45 and 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 are exact divisors of 126.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 45 and 126 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 45 and also of 126.
Steps to find Factors of 45 and 126
- Step 1. Find all the numbers that would divide 45 and 126 without leaving any remainder. Starting with the number 1 upto 22 (half of 45) and 1 upto 63 (half of 126). The number 1 and the number itself are always factors of the given number.
45 ÷ 1 : Remainder = 0
126 ÷ 1 : Remainder = 0
45 ÷ 3 : Remainder = 0
126 ÷ 2 : Remainder = 0
45 ÷ 5 : Remainder = 0
126 ÷ 3 : Remainder = 0
45 ÷ 9 : Remainder = 0
126 ÷ 6 : Remainder = 0
45 ÷ 15 : Remainder = 0
126 ÷ 7 : Remainder = 0
45 ÷ 45 : Remainder = 0
126 ÷ 9 : Remainder = 0
126 ÷ 126 : Remainder = 0
Hence, Factors of
45 are 1, 3, 5, 9, 15, and 45
And, Factors of
126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126
Examples of GCF
Sammy baked 45 chocolate cookies and 126 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 45 and 126.
GCF of 45 and 126 is 9.
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(45, 126) = ( 45 * 126 ) / LCM(45, 126) = 9.
What is the GCF of 45 and 126?GCF of 45 and 126 is 9.
Ram has 45 cans of Pepsi and 126 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 45 and 126. Hence GCF of 45 and 126 is 9. So the number of tables that can be arranged is 9.
Rubel is creating individual servings of starters for her birthday party. He has 45 pizzas and 126 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 45 and 126. Thus GCF of 45 and 126 is 9.
Ariel is making ready to eat meals to share with friends. She has 45 bottles of water and 126 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 45 and 126. So the GCF of 45 and 126 is 9.
Mary has 45 blue buttons and 126 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 45 and 126. Hence, the GCF of 45 and 126 or the greatest arrangement is 9.
Kamal is making identical balloon arrangements for a party. He has 45 maroon balloons, and 126 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 45 and 126. So the GCF of 45 and 126 is 9.