How can we define factors?
In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 176 and 189 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 176 and also of 189.
- Every number is a factor of zero (0), since 176 x 0 = 0 and 189 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, 8, 11, 16, 22, 44, 88, 176 are exact divisors of 176 and 1, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189.
- Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. Each factor divides 176 without leaving a remainder.
Simlarly, factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. Each factor divides 189 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 11, 16, 22, 44, 88, 176 are all less than or equal to 176 and 1, 3, 7, 9, 21, 27, 63, 189 are all less than or equal to 189.
Steps to find Factors of 176 and 189
- Step 1. Find all the numbers that would divide 176 and 189 without leaving any remainder. Starting with the number 1 upto 88 (half of 176) and 1 upto 94 (half of 189). The number 1 and the number itself are always factors of the given number.
176 ÷ 1 : Remainder = 0
189 ÷ 1 : Remainder = 0
176 ÷ 2 : Remainder = 0
189 ÷ 3 : Remainder = 0
176 ÷ 4 : Remainder = 0
189 ÷ 7 : Remainder = 0
176 ÷ 8 : Remainder = 0
189 ÷ 9 : Remainder = 0
176 ÷ 11 : Remainder = 0
189 ÷ 21 : Remainder = 0
176 ÷ 16 : Remainder = 0
189 ÷ 27 : Remainder = 0
176 ÷ 22 : Remainder = 0
189 ÷ 63 : Remainder = 0
176 ÷ 44 : Remainder = 0
189 ÷ 189 : Remainder = 0
176 ÷ 176 : Remainder = 0
Hence, Factors of
176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176
And, Factors of
189 are 1, 3, 7, 9, 21, 27, 63, and 189
Examples of GCF
Sammy baked 176 chocolate cookies and 189 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 176 and 189.
GCF of 176 and 189 is 1.
A class has 176 boys and 189 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 176 and 189. Hence, GCF of 176 and 189 is 1.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(176, 189) = ( 176 * 189 ) / LCM(176, 189) = 1.
What is the GCF of 176 and 189?GCF of 176 and 189 is 1.
Ram has 176 cans of Pepsi and 189 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 176 and 189. Hence GCF of 176 and 189 is 1. So the number of tables that can be arranged is 1.
Rubel is creating individual servings of starters for her birthday party. He has 176 pizzas and 189 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 176 and 189. Thus GCF of 176 and 189 is 1.
Ariel is making ready to eat meals to share with friends. She has 176 bottles of water and 189 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 176 and 189. So the GCF of 176 and 189 is 1.
Kamal is making identical balloon arrangements for a party. He has 176 maroon balloons, and 189 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 176 and 189. So the GCF of 176 and 189 is 1.
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 176 bus tickets and 189 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 176 and 189. Hence, GCF of 176 and 189 is 1.