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 (140, 600).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 140 and 600 is 20, where 20 is less than both 140 and 600.
- 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.
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. 140 and 600 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 140 and also of 600.
- Every number is a factor of zero (0), since 140 x 0 = 0 and 600 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, 5, 7, 10, 14, 20, 28, 35, 70, 140 are exact divisors of 140 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 are exact divisors of 600.
- Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. Each factor divides 140 without leaving a remainder.
Simlarly, factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600. Each factor divides 600 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 are all less than or equal to 140 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 are all less than or equal to 600.
Steps to find Factors of 140 and 600
- Step 1. Find all the numbers that would divide 140 and 600 without leaving any remainder. Starting with the number 1 upto 70 (half of 140) and 1 upto 300 (half of 600). The number 1 and the number itself are always factors of the given number.
140 ÷ 1 : Remainder = 0
600 ÷ 1 : Remainder = 0
140 ÷ 2 : Remainder = 0
600 ÷ 2 : Remainder = 0
140 ÷ 4 : Remainder = 0
600 ÷ 3 : Remainder = 0
140 ÷ 5 : Remainder = 0
600 ÷ 4 : Remainder = 0
140 ÷ 7 : Remainder = 0
600 ÷ 5 : Remainder = 0
140 ÷ 10 : Remainder = 0
600 ÷ 6 : Remainder = 0
140 ÷ 14 : Remainder = 0
600 ÷ 8 : Remainder = 0
140 ÷ 20 : Remainder = 0
600 ÷ 10 : Remainder = 0
140 ÷ 28 : Remainder = 0
600 ÷ 12 : Remainder = 0
140 ÷ 35 : Remainder = 0
600 ÷ 15 : Remainder = 0
140 ÷ 70 : Remainder = 0
600 ÷ 20 : Remainder = 0
140 ÷ 140 : Remainder = 0
600 ÷ 24 : Remainder = 0
600 ÷ 100 : Remainder = 0
600 ÷ 120 : Remainder = 0
600 ÷ 150 : Remainder = 0
600 ÷ 200 : Remainder = 0
600 ÷ 300 : Remainder = 0
600 ÷ 600 : Remainder = 0
Hence, Factors of
140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140
And, Factors of
600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600
Examples of GCF
Sammy baked 140 chocolate cookies and 600 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 140 and 600.
GCF of 140 and 600 is 20.
A class has 140 boys and 600 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 140 and 600. Hence, GCF of 140 and 600 is 20.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(140, 600) = ( 140 * 600 ) / LCM(140, 600) = 20.
What is the GCF of 140 and 600?GCF of 140 and 600 is 20.
Ram has 140 cans of Pepsi and 600 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 140 and 600. Hence GCF of 140 and 600 is 20. So the number of tables that can be arranged is 20.
Rubel is creating individual servings of starters for her birthday party. He has 140 pizzas and 600 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 140 and 600. Thus GCF of 140 and 600 is 20.
Ariel is making ready to eat meals to share with friends. She has 140 bottles of water and 600 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 140 and 600. So the GCF of 140 and 600 is 20.
Kamal is making identical balloon arrangements for a party. He has 140 maroon balloons, and 600 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 140 and 600. So the GCF of 140 and 600 is 20.
To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 140 bus tickets and 600 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?To make the greatest number of envelopes Abir needs to find out the GCF of 140 and 600. Hence, GCF of 140 and 600 is 20.