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 (450, 750).
Properties of GCF
- Given two numbers 450 and 750, such that GCF is 150 where 150 will always be less than 450 and 750.
- GCF of two numbers is always equal to 1 in case given numbers are consecutive.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.
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
- Each number is a factor of itself. Eg. 450 and 750 are factors of themselves respectively.
- 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, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450 are exact divisors of 450 and 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750 are exact divisors of 750.
- 1 is a factor of every number. Eg. 1 is a factor of 450 and also of 750.
- Every number is a factor of zero (0), since 450 x 0 = 0 and 750 x 0 = 0.
Steps to find Factors of 450 and 750
- Step 1. Find all the numbers that would divide 450 and 750 without leaving any remainder. Starting with the number 1 upto 225 (half of 450) and 1 upto 375 (half of 750). The number 1 and the number itself are always factors of the given number.
450 ÷ 1 : Remainder = 0
750 ÷ 1 : Remainder = 0
450 ÷ 2 : Remainder = 0
750 ÷ 2 : Remainder = 0
450 ÷ 3 : Remainder = 0
750 ÷ 3 : Remainder = 0
450 ÷ 5 : Remainder = 0
750 ÷ 5 : Remainder = 0
450 ÷ 6 : Remainder = 0
750 ÷ 6 : Remainder = 0
450 ÷ 9 : Remainder = 0
750 ÷ 10 : Remainder = 0
450 ÷ 10 : Remainder = 0
750 ÷ 15 : Remainder = 0
450 ÷ 15 : Remainder = 0
750 ÷ 25 : Remainder = 0
450 ÷ 18 : Remainder = 0
750 ÷ 30 : Remainder = 0
450 ÷ 25 : Remainder = 0
750 ÷ 50 : Remainder = 0
450 ÷ 30 : Remainder = 0
750 ÷ 75 : Remainder = 0
450 ÷ 45 : Remainder = 0
750 ÷ 125 : Remainder = 0
450 ÷ 50 : Remainder = 0
750 ÷ 150 : Remainder = 0
450 ÷ 75 : Remainder = 0
750 ÷ 250 : Remainder = 0
450 ÷ 90 : Remainder = 0
750 ÷ 375 : Remainder = 0
450 ÷ 150 : Remainder = 0
750 ÷ 750 : Remainder = 0
450 ÷ 225 : Remainder = 0
450 ÷ 450 : Remainder = 0
Hence, Factors of
450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450
And, Factors of
750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750
Examples of GCF
Sammy baked 450 chocolate cookies and 750 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 450 and 750.
GCF of 450 and 750 is 150.
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(450, 750) = ( 450 * 750 ) / LCM(450, 750) = 150.
What is the GCF of 450 and 750?GCF of 450 and 750 is 150.
Ram has 450 cans of Pepsi and 750 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 450 and 750. Hence GCF of 450 and 750 is 150. So the number of tables that can be arranged is 150.
Rubel is creating individual servings of starters for her birthday party. He has 450 pizzas and 750 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 450 and 750. Thus GCF of 450 and 750 is 150.
Ariel is making ready to eat meals to share with friends. She has 450 bottles of water and 750 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 450 and 750. So the GCF of 450 and 750 is 150.
Mary has 450 blue buttons and 750 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 450 and 750. Hence, the GCF of 450 and 750 or the greatest arrangement is 150.
Kamal is making identical balloon arrangements for a party. He has 450 maroon balloons, and 750 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 450 and 750. So the GCF of 450 and 750 is 150.