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. 2352 and 1323 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 2352 and also of 1323.
- Every number is a factor of zero (0), since 2352 x 0 = 0 and 1323 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, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352 are exact divisors of 2352 and 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323 are exact divisors of 1323.
- Factors of 2352 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352. Each factor divides 2352 without leaving a remainder.
Simlarly, factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323. Each factor divides 1323 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352 are all less than or equal to 2352 and 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323 are all less than or equal to 1323.
Steps to find Factors of 2352 and 1323
- Step 1. Find all the numbers that would divide 2352 and 1323 without leaving any remainder. Starting with the number 1 upto 1176 (half of 2352) and 1 upto 661 (half of 1323). The number 1 and the number itself are always factors of the given number.
2352 ÷ 1 : Remainder = 0
1323 ÷ 1 : Remainder = 0
2352 ÷ 2 : Remainder = 0
1323 ÷ 3 : Remainder = 0
2352 ÷ 3 : Remainder = 0
1323 ÷ 7 : Remainder = 0
2352 ÷ 4 : Remainder = 0
1323 ÷ 9 : Remainder = 0
2352 ÷ 6 : Remainder = 0
1323 ÷ 21 : Remainder = 0
2352 ÷ 7 : Remainder = 0
1323 ÷ 27 : Remainder = 0
2352 ÷ 8 : Remainder = 0
1323 ÷ 49 : Remainder = 0
2352 ÷ 12 : Remainder = 0
1323 ÷ 63 : Remainder = 0
2352 ÷ 14 : Remainder = 0
1323 ÷ 147 : Remainder = 0
2352 ÷ 16 : Remainder = 0
1323 ÷ 189 : Remainder = 0
2352 ÷ 21 : Remainder = 0
1323 ÷ 441 : Remainder = 0
2352 ÷ 24 : Remainder = 0
1323 ÷ 1323 : Remainder = 0
2352 ÷ 28 : Remainder = 0
2352 ÷ 42 : Remainder = 0
2352 ÷ 48 : Remainder = 0
2352 ÷ 49 : Remainder = 0
2352 ÷ 56 : Remainder = 0
2352 ÷ 84 : Remainder = 0
2352 ÷ 98 : Remainder = 0
2352 ÷ 112 : Remainder = 0
2352 ÷ 147 : Remainder = 0
2352 ÷ 168 : Remainder = 0
2352 ÷ 196 : Remainder = 0
2352 ÷ 294 : Remainder = 0
2352 ÷ 336 : Remainder = 0
2352 ÷ 392 : Remainder = 0
2352 ÷ 588 : Remainder = 0
2352 ÷ 784 : Remainder = 0
2352 ÷ 1176 : Remainder = 0
2352 ÷ 2352 : Remainder = 0
Hence, Factors of
2352 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, and 2352
And, Factors of
1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, and 1323
Examples of GCF
Sammy baked 2352 chocolate cookies and 1323 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 2352 and 1323.
GCF of 2352 and 1323 is 147.
A class has 2352 boys and 1323 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 2352 and 1323. Hence, GCF of 2352 and 1323 is 147.
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.
Ram has 2352 cans of Pepsi and 1323 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 2352 and 1323. Hence GCF of 2352 and 1323 is 147. So the number of tables that can be arranged is 147.
Ariel is making ready to eat meals to share with friends. She has 2352 bottles of water and 1323 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 2352 and 1323. So the GCF of 2352 and 1323 is 147.
Mary has 2352 blue buttons and 1323 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 2352 and 1323. Hence, the GCF of 2352 and 1323 or the greatest arrangement is 147.
Kamal is making identical balloon arrangements for a party. He has 2352 maroon balloons, and 1323 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 2352 and 1323. So the GCF of 2352 and 1323 is 147.
Kunal is making baskets full of nuts and dried fruits. He has 2352 bags of nuts and 1323 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 2352 and 1323. So the GCF of 2352 and 1323 is 147.
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 2352 bus tickets and 1323 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 2352 and 1323. Hence, GCF of 2352 and 1323 is 147.