How do you explain factors?
In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 1152 and 1664 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1152 and also of 1664.
- Every number is a factor of zero (0), since 1152 x 0 = 0 and 1664 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, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152 are exact divisors of 1152 and 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 are exact divisors of 1664.
- Factors of 1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152. Each factor divides 1152 without leaving a remainder.
Simlarly, factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664. Each factor divides 1664 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152 are all less than or equal to 1152 and 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 are all less than or equal to 1664.
Steps to find Factors of 1152 and 1664
- Step 1. Find all the numbers that would divide 1152 and 1664 without leaving any remainder. Starting with the number 1 upto 576 (half of 1152) and 1 upto 832 (half of 1664). The number 1 and the number itself are always factors of the given number.
1152 ÷ 1 : Remainder = 0
1664 ÷ 1 : Remainder = 0
1152 ÷ 2 : Remainder = 0
1664 ÷ 2 : Remainder = 0
1152 ÷ 3 : Remainder = 0
1664 ÷ 4 : Remainder = 0
1152 ÷ 4 : Remainder = 0
1664 ÷ 8 : Remainder = 0
1152 ÷ 6 : Remainder = 0
1664 ÷ 13 : Remainder = 0
1152 ÷ 8 : Remainder = 0
1664 ÷ 16 : Remainder = 0
1152 ÷ 9 : Remainder = 0
1664 ÷ 26 : Remainder = 0
1152 ÷ 12 : Remainder = 0
1664 ÷ 32 : Remainder = 0
1152 ÷ 16 : Remainder = 0
1664 ÷ 52 : Remainder = 0
1152 ÷ 18 : Remainder = 0
1664 ÷ 64 : Remainder = 0
1152 ÷ 24 : Remainder = 0
1664 ÷ 104 : Remainder = 0
1152 ÷ 32 : Remainder = 0
1664 ÷ 128 : Remainder = 0
1152 ÷ 36 : Remainder = 0
1664 ÷ 208 : Remainder = 0
1152 ÷ 48 : Remainder = 0
1664 ÷ 416 : Remainder = 0
1152 ÷ 64 : Remainder = 0
1664 ÷ 832 : Remainder = 0
1152 ÷ 72 : Remainder = 0
1664 ÷ 1664 : Remainder = 0
1152 ÷ 96 : Remainder = 0
1152 ÷ 128 : Remainder = 0
1152 ÷ 144 : Remainder = 0
1152 ÷ 192 : Remainder = 0
1152 ÷ 288 : Remainder = 0
1152 ÷ 384 : Remainder = 0
1152 ÷ 576 : Remainder = 0
1152 ÷ 1152 : Remainder = 0
Hence, Factors of
1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, and 1152
And, Factors of
1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, and 1664
Examples of GCF
Sammy baked 1152 chocolate cookies and 1664 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 1152 and 1664.
GCF of 1152 and 1664 is 128.
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(1152, 1664) = ( 1152 * 1664 ) / LCM(1152, 1664) = 128.
What is the GCF of 1152 and 1664?GCF of 1152 and 1664 is 128.
Ram has 1152 cans of Pepsi and 1664 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 1152 and 1664. Hence GCF of 1152 and 1664 is 128. So the number of tables that can be arranged is 128.
Rubel is creating individual servings of starters for her birthday party. He has 1152 pizzas and 1664 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 1152 and 1664. Thus GCF of 1152 and 1664 is 128.
Ariel is making ready to eat meals to share with friends. She has 1152 bottles of water and 1664 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 1152 and 1664. So the GCF of 1152 and 1664 is 128.
Mary has 1152 blue buttons and 1664 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 1152 and 1664. Hence, the GCF of 1152 and 1664 or the greatest arrangement is 128.
Kamal is making identical balloon arrangements for a party. He has 1152 maroon balloons, and 1664 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 1152 and 1664. So the GCF of 1152 and 1664 is 128.