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. 2040 and 1100 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 2040 and also of 1100.
- Every number is a factor of zero (0), since 2040 x 0 = 0 and 1100 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, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040 are exact divisors of 2040 and 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 are exact divisors of 1100.
- Factors of 2040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040. Each factor divides 2040 without leaving a remainder.
Simlarly, factors of 1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100. Each factor divides 1100 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040 are all less than or equal to 2040 and 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100 are all less than or equal to 1100.
Steps to find Factors of 2040 and 1100
- Step 1. Find all the numbers that would divide 2040 and 1100 without leaving any remainder. Starting with the number 1 upto 1020 (half of 2040) and 1 upto 550 (half of 1100). The number 1 and the number itself are always factors of the given number.
2040 ÷ 1 : Remainder = 0
1100 ÷ 1 : Remainder = 0
2040 ÷ 2 : Remainder = 0
1100 ÷ 2 : Remainder = 0
2040 ÷ 3 : Remainder = 0
1100 ÷ 4 : Remainder = 0
2040 ÷ 4 : Remainder = 0
1100 ÷ 5 : Remainder = 0
2040 ÷ 5 : Remainder = 0
1100 ÷ 10 : Remainder = 0
2040 ÷ 6 : Remainder = 0
1100 ÷ 11 : Remainder = 0
2040 ÷ 8 : Remainder = 0
1100 ÷ 20 : Remainder = 0
2040 ÷ 10 : Remainder = 0
1100 ÷ 22 : Remainder = 0
2040 ÷ 12 : Remainder = 0
1100 ÷ 25 : Remainder = 0
2040 ÷ 15 : Remainder = 0
1100 ÷ 44 : Remainder = 0
2040 ÷ 17 : Remainder = 0
1100 ÷ 50 : Remainder = 0
2040 ÷ 20 : Remainder = 0
1100 ÷ 55 : Remainder = 0
2040 ÷ 24 : Remainder = 0
1100 ÷ 100 : Remainder = 0
2040 ÷ 30 : Remainder = 0
1100 ÷ 110 : Remainder = 0
2040 ÷ 34 : Remainder = 0
1100 ÷ 220 : Remainder = 0
2040 ÷ 40 : Remainder = 0
1100 ÷ 275 : Remainder = 0
2040 ÷ 51 : Remainder = 0
1100 ÷ 550 : Remainder = 0
2040 ÷ 60 : Remainder = 0
1100 ÷ 1100 : Remainder = 0
2040 ÷ 68 : Remainder = 0
2040 ÷ 85 : Remainder = 0
2040 ÷ 102 : Remainder = 0
2040 ÷ 120 : Remainder = 0
2040 ÷ 136 : Remainder = 0
2040 ÷ 170 : Remainder = 0
2040 ÷ 204 : Remainder = 0
2040 ÷ 255 : Remainder = 0
2040 ÷ 340 : Remainder = 0
2040 ÷ 408 : Remainder = 0
2040 ÷ 510 : Remainder = 0
2040 ÷ 680 : Remainder = 0
2040 ÷ 1020 : Remainder = 0
2040 ÷ 2040 : Remainder = 0
Hence, Factors of
2040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, and 2040
And, Factors of
1100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, and 1100
Examples of GCF
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(2040, 1100) = ( 2040 * 1100 ) / LCM(2040, 1100) = 20.
What is the GCF of 2040 and 1100?GCF of 2040 and 1100 is 20.
Ram has 2040 cans of Pepsi and 1100 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 2040 and 1100. Hence GCF of 2040 and 1100 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 2040 pizzas and 1100 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 2040 and 1100. Thus GCF of 2040 and 1100 is 20.
Ariel is making ready to eat meals to share with friends. She has 2040 bottles of water and 1100 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 2040 and 1100. So the GCF of 2040 and 1100 is 20.
Mary has 2040 blue buttons and 1100 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 2040 and 1100. Hence, the GCF of 2040 and 1100 or the greatest arrangement is 20.
Kamal is making identical balloon arrangements for a party. He has 2040 maroon balloons, and 1100 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 2040 and 1100. So the GCF of 2040 and 1100 is 20.
Kunal is making baskets full of nuts and dried fruits. He has 2040 bags of nuts and 1100 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 2040 and 1100. So the GCF of 2040 and 1100 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 2040 bus tickets and 1100 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 2040 and 1100. Hence, GCF of 2040 and 1100 is 20.