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. 3240 and 960 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 3240 and also of 960.
- Every number is a factor of zero (0), since 3240 x 0 = 0 and 960 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, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 are exact divisors of 3240 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 are exact divisors of 960.
- Factors of 3240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240. Each factor divides 3240 without leaving a remainder.
Simlarly, factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960. Each factor divides 960 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, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 are all less than or equal to 3240 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960 are all less than or equal to 960.
Steps to find Factors of 3240 and 960
- Step 1. Find all the numbers that would divide 3240 and 960 without leaving any remainder. Starting with the number 1 upto 1620 (half of 3240) and 1 upto 480 (half of 960). The number 1 and the number itself are always factors of the given number.
3240 ÷ 1 : Remainder = 0
960 ÷ 1 : Remainder = 0
3240 ÷ 2 : Remainder = 0
960 ÷ 2 : Remainder = 0
3240 ÷ 3 : Remainder = 0
960 ÷ 3 : Remainder = 0
3240 ÷ 4 : Remainder = 0
960 ÷ 4 : Remainder = 0
3240 ÷ 5 : Remainder = 0
960 ÷ 5 : Remainder = 0
3240 ÷ 6 : Remainder = 0
960 ÷ 6 : Remainder = 0
3240 ÷ 8 : Remainder = 0
960 ÷ 8 : Remainder = 0
3240 ÷ 9 : Remainder = 0
960 ÷ 10 : Remainder = 0
3240 ÷ 10 : Remainder = 0
960 ÷ 12 : Remainder = 0
3240 ÷ 12 : Remainder = 0
960 ÷ 15 : Remainder = 0
3240 ÷ 15 : Remainder = 0
960 ÷ 16 : Remainder = 0
3240 ÷ 18 : Remainder = 0
960 ÷ 20 : Remainder = 0
3240 ÷ 20 : Remainder = 0
960 ÷ 24 : Remainder = 0
3240 ÷ 24 : Remainder = 0
960 ÷ 30 : Remainder = 0
3240 ÷ 27 : Remainder = 0
960 ÷ 32 : Remainder = 0
3240 ÷ 30 : Remainder = 0
960 ÷ 40 : Remainder = 0
3240 ÷ 36 : Remainder = 0
960 ÷ 48 : Remainder = 0
3240 ÷ 40 : Remainder = 0
960 ÷ 60 : Remainder = 0
3240 ÷ 45 : Remainder = 0
960 ÷ 64 : Remainder = 0
3240 ÷ 54 : Remainder = 0
960 ÷ 80 : Remainder = 0
3240 ÷ 60 : Remainder = 0
960 ÷ 96 : Remainder = 0
3240 ÷ 72 : Remainder = 0
960 ÷ 120 : Remainder = 0
3240 ÷ 81 : Remainder = 0
960 ÷ 160 : Remainder = 0
3240 ÷ 90 : Remainder = 0
960 ÷ 192 : Remainder = 0
3240 ÷ 108 : Remainder = 0
960 ÷ 240 : Remainder = 0
3240 ÷ 120 : Remainder = 0
960 ÷ 320 : Remainder = 0
3240 ÷ 135 : Remainder = 0
960 ÷ 480 : Remainder = 0
3240 ÷ 162 : Remainder = 0
960 ÷ 960 : Remainder = 0
3240 ÷ 180 : Remainder = 0
3240 ÷ 216 : Remainder = 0
3240 ÷ 270 : Remainder = 0
3240 ÷ 324 : Remainder = 0
3240 ÷ 360 : Remainder = 0
3240 ÷ 405 : Remainder = 0
3240 ÷ 540 : Remainder = 0
3240 ÷ 648 : Remainder = 0
3240 ÷ 810 : Remainder = 0
3240 ÷ 1080 : Remainder = 0
3240 ÷ 1620 : Remainder = 0
3240 ÷ 3240 : Remainder = 0
Hence, Factors of
3240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, and 3240
And, Factors of
960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960
Examples of GCF
Sammy baked 3240 chocolate cookies and 960 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 3240 and 960.
GCF of 3240 and 960 is 120.
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(3240, 960) = ( 3240 * 960 ) / LCM(3240, 960) = 120.
What is the GCF of 3240 and 960?GCF of 3240 and 960 is 120.
Ram has 3240 cans of Pepsi and 960 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 3240 and 960. Hence GCF of 3240 and 960 is 120. So the number of tables that can be arranged is 120.
Rubel is creating individual servings of starters for her birthday party. He has 3240 pizzas and 960 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 3240 and 960. Thus GCF of 3240 and 960 is 120.
Ariel is making ready to eat meals to share with friends. She has 3240 bottles of water and 960 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 3240 and 960. So the GCF of 3240 and 960 is 120.
Mary has 3240 blue buttons and 960 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 3240 and 960. Hence, the GCF of 3240 and 960 or the greatest arrangement is 120.
Kamal is making identical balloon arrangements for a party. He has 3240 maroon balloons, and 960 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 3240 and 960. So the GCF of 3240 and 960 is 120.