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. 212 and 312 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 212 and also of 312.
- Every number is a factor of zero (0), since 212 x 0 = 0 and 312 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, 4, 53, 106, 212 are exact divisors of 212 and 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312 are exact divisors of 312.
- Factors of 212 are 1, 2, 4, 53, 106, 212. Each factor divides 212 without leaving a remainder.
Simlarly, factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. Each factor divides 312 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 53, 106, 212 are all less than or equal to 212 and 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312 are all less than or equal to 312.
Steps to find Factors of 212 and 312
- Step 1. Find all the numbers that would divide 212 and 312 without leaving any remainder. Starting with the number 1 upto 106 (half of 212) and 1 upto 156 (half of 312). The number 1 and the number itself are always factors of the given number.
212 ÷ 1 : Remainder = 0
312 ÷ 1 : Remainder = 0
212 ÷ 2 : Remainder = 0
312 ÷ 2 : Remainder = 0
212 ÷ 4 : Remainder = 0
312 ÷ 3 : Remainder = 0
212 ÷ 53 : Remainder = 0
312 ÷ 4 : Remainder = 0
212 ÷ 106 : Remainder = 0
312 ÷ 6 : Remainder = 0
212 ÷ 212 : Remainder = 0
312 ÷ 8 : Remainder = 0
312 ÷ 104 : Remainder = 0
312 ÷ 156 : Remainder = 0
312 ÷ 312 : Remainder = 0
Hence, Factors of
212 are 1, 2, 4, 53, 106, and 212
And, Factors of
312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312
Examples of GCF
Sammy baked 212 chocolate cookies and 312 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 212 and 312.
GCF of 212 and 312 is 4.
A class has 212 boys and 312 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 212 and 312. Hence, GCF of 212 and 312 is 4.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(212, 312) = ( 212 * 312 ) / LCM(212, 312) = 4.
What is the GCF of 212 and 312?GCF of 212 and 312 is 4.
Ram has 212 cans of Pepsi and 312 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 212 and 312. Hence GCF of 212 and 312 is 4. So the number of tables that can be arranged is 4.
Rubel is creating individual servings of starters for her birthday party. He has 212 pizzas and 312 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 212 and 312. Thus GCF of 212 and 312 is 4.
Ariel is making ready to eat meals to share with friends. She has 212 bottles of water and 312 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 212 and 312. So the GCF of 212 and 312 is 4.
Kamal is making identical balloon arrangements for a party. He has 212 maroon balloons, and 312 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 212 and 312. So the GCF of 212 and 312 is 4.
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 212 bus tickets and 312 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 212 and 312. Hence, GCF of 212 and 312 is 4.