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. 2760 and 2025 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 2760 and also of 2025.
- Every number is a factor of zero (0), since 2760 x 0 = 0 and 2025 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, 20, 23, 24, 30, 40, 46, 60, 69, 92, 115, 120, 138, 184, 230, 276, 345, 460, 552, 690, 920, 1380, 2760 are exact divisors of 2760 and 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025 are exact divisors of 2025.
- Factors of 2760 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 30, 40, 46, 60, 69, 92, 115, 120, 138, 184, 230, 276, 345, 460, 552, 690, 920, 1380, 2760. Each factor divides 2760 without leaving a remainder.
Simlarly, factors of 2025 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025. Each factor divides 2025 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, 20, 23, 24, 30, 40, 46, 60, 69, 92, 115, 120, 138, 184, 230, 276, 345, 460, 552, 690, 920, 1380, 2760 are all less than or equal to 2760 and 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025 are all less than or equal to 2025.
Steps to find Factors of 2760 and 2025
- Step 1. Find all the numbers that would divide 2760 and 2025 without leaving any remainder. Starting with the number 1 upto 1380 (half of 2760) and 1 upto 1012 (half of 2025). The number 1 and the number itself are always factors of the given number.
2760 ÷ 1 : Remainder = 0
2025 ÷ 1 : Remainder = 0
2760 ÷ 2 : Remainder = 0
2025 ÷ 3 : Remainder = 0
2760 ÷ 3 : Remainder = 0
2025 ÷ 5 : Remainder = 0
2760 ÷ 4 : Remainder = 0
2025 ÷ 9 : Remainder = 0
2760 ÷ 5 : Remainder = 0
2025 ÷ 15 : Remainder = 0
2760 ÷ 6 : Remainder = 0
2025 ÷ 25 : Remainder = 0
2760 ÷ 8 : Remainder = 0
2025 ÷ 27 : Remainder = 0
2760 ÷ 10 : Remainder = 0
2025 ÷ 45 : Remainder = 0
2760 ÷ 12 : Remainder = 0
2025 ÷ 75 : Remainder = 0
2760 ÷ 15 : Remainder = 0
2025 ÷ 81 : Remainder = 0
2760 ÷ 20 : Remainder = 0
2025 ÷ 135 : Remainder = 0
2760 ÷ 23 : Remainder = 0
2025 ÷ 225 : Remainder = 0
2760 ÷ 24 : Remainder = 0
2025 ÷ 405 : Remainder = 0
2760 ÷ 30 : Remainder = 0
2025 ÷ 675 : Remainder = 0
2760 ÷ 40 : Remainder = 0
2025 ÷ 2025 : Remainder = 0
2760 ÷ 46 : Remainder = 0
2760 ÷ 60 : Remainder = 0
2760 ÷ 69 : Remainder = 0
2760 ÷ 92 : Remainder = 0
2760 ÷ 115 : Remainder = 0
2760 ÷ 120 : Remainder = 0
2760 ÷ 138 : Remainder = 0
2760 ÷ 184 : Remainder = 0
2760 ÷ 230 : Remainder = 0
2760 ÷ 276 : Remainder = 0
2760 ÷ 345 : Remainder = 0
2760 ÷ 460 : Remainder = 0
2760 ÷ 552 : Remainder = 0
2760 ÷ 690 : Remainder = 0
2760 ÷ 920 : Remainder = 0
2760 ÷ 1380 : Remainder = 0
2760 ÷ 2760 : Remainder = 0
Hence, Factors of
2760 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 30, 40, 46, 60, 69, 92, 115, 120, 138, 184, 230, 276, 345, 460, 552, 690, 920, 1380, and 2760
And, Factors of
2025 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, and 2025
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(2760, 2025) = ( 2760 * 2025 ) / LCM(2760, 2025) = 15.
What is the GCF of 2760 and 2025?GCF of 2760 and 2025 is 15.
Ram has 2760 cans of Pepsi and 2025 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 2760 and 2025. Hence GCF of 2760 and 2025 is 15. So the number of tables that can be arranged is 15.
Rubel is creating individual servings of starters for her birthday party. He has 2760 pizzas and 2025 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 2760 and 2025. Thus GCF of 2760 and 2025 is 15.
Ariel is making ready to eat meals to share with friends. She has 2760 bottles of water and 2025 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 2760 and 2025. So the GCF of 2760 and 2025 is 15.
Mary has 2760 blue buttons and 2025 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 2760 and 2025. Hence, the GCF of 2760 and 2025 or the greatest arrangement is 15.
Kamal is making identical balloon arrangements for a party. He has 2760 maroon balloons, and 2025 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 2760 and 2025. So the GCF of 2760 and 2025 is 15.
Kunal is making baskets full of nuts and dried fruits. He has 2760 bags of nuts and 2025 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 2760 and 2025. So the GCF of 2760 and 2025 is 15.
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 2760 bus tickets and 2025 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 2760 and 2025. Hence, GCF of 2760 and 2025 is 15.