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 (280, 490).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 280 and 490 is 70, where 70 is less than both 280 and 490.
- 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. 280 and 490 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 280 and also of 490.
- Every number is a factor of zero (0), since 280 x 0 = 0 and 490 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, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280 are exact divisors of 280 and 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 are exact divisors of 490.
- Factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. Each factor divides 280 without leaving a remainder.
Simlarly, factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490. Each factor divides 490 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280 are all less than or equal to 280 and 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 are all less than or equal to 490.
Steps to find Factors of 280 and 490
- Step 1. Find all the numbers that would divide 280 and 490 without leaving any remainder. Starting with the number 1 upto 140 (half of 280) and 1 upto 245 (half of 490). The number 1 and the number itself are always factors of the given number.
280 ÷ 1 : Remainder = 0
490 ÷ 1 : Remainder = 0
280 ÷ 2 : Remainder = 0
490 ÷ 2 : Remainder = 0
280 ÷ 4 : Remainder = 0
490 ÷ 5 : Remainder = 0
280 ÷ 5 : Remainder = 0
490 ÷ 7 : Remainder = 0
280 ÷ 7 : Remainder = 0
490 ÷ 10 : Remainder = 0
280 ÷ 8 : Remainder = 0
490 ÷ 14 : Remainder = 0
280 ÷ 10 : Remainder = 0
490 ÷ 35 : Remainder = 0
280 ÷ 14 : Remainder = 0
490 ÷ 49 : Remainder = 0
280 ÷ 20 : Remainder = 0
490 ÷ 70 : Remainder = 0
280 ÷ 28 : Remainder = 0
490 ÷ 98 : Remainder = 0
280 ÷ 35 : Remainder = 0
490 ÷ 245 : Remainder = 0
280 ÷ 40 : Remainder = 0
490 ÷ 490 : Remainder = 0
280 ÷ 140 : Remainder = 0
280 ÷ 280 : Remainder = 0
Hence, Factors of
280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280
And, Factors of
490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490
Examples of GCF
Sammy baked 280 chocolate cookies and 490 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 280 and 490.
GCF of 280 and 490 is 70.
A class has 280 boys and 490 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 280 and 490. Hence, GCF of 280 and 490 is 70.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(280, 490) = ( 280 * 490 ) / LCM(280, 490) = 70.
What is the GCF of 280 and 490?GCF of 280 and 490 is 70.
Ram has 280 cans of Pepsi and 490 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 280 and 490. Hence GCF of 280 and 490 is 70. So the number of tables that can be arranged is 70.
Mary has 280 blue buttons and 490 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 280 and 490. Hence, the GCF of 280 and 490 or the greatest arrangement is 70.
Kamal is making identical balloon arrangements for a party. He has 280 maroon balloons, and 490 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 280 and 490. So the GCF of 280 and 490 is 70.
Kunal is making baskets full of nuts and dried fruits. He has 280 bags of nuts and 490 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 280 and 490. So the GCF of 280 and 490 is 70.
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 280 bus tickets and 490 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 280 and 490. Hence, GCF of 280 and 490 is 70.