What is the definition of factors?
In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 28 and 32 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 28 and also of 32.
- Every number is a factor of zero (0), since 28 x 0 = 0 and 32 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, 7, 14, 28 are exact divisors of 28 and 1, 2, 4, 8, 16, 32 are exact divisors of 32.
- Factors of 28 are 1, 2, 4, 7, 14, 28. Each factor divides 28 without leaving a remainder.
Simlarly, factors of 32 are 1, 2, 4, 8, 16, 32. Each factor divides 32 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 28 are all less than or equal to 28 and 1, 2, 4, 8, 16, 32 are all less than or equal to 32.
Steps to find Factors of 28 and 32
- Step 1. Find all the numbers that would divide 28 and 32 without leaving any remainder. Starting with the number 1 upto 14 (half of 28) and 1 upto 16 (half of 32). The number 1 and the number itself are always factors of the given number.
28 ÷ 1 : Remainder = 0
32 ÷ 1 : Remainder = 0
28 ÷ 2 : Remainder = 0
32 ÷ 2 : Remainder = 0
28 ÷ 4 : Remainder = 0
32 ÷ 4 : Remainder = 0
28 ÷ 7 : Remainder = 0
32 ÷ 8 : Remainder = 0
28 ÷ 14 : Remainder = 0
32 ÷ 16 : Remainder = 0
28 ÷ 28 : Remainder = 0
32 ÷ 32 : Remainder = 0
Hence, Factors of
28 are 1, 2, 4, 7, 14, and 28
And, Factors of
32 are 1, 2, 4, 8, 16, and 32
Examples of GCF
Sammy baked 28 chocolate cookies and 32 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 28 and 32.
GCF of 28 and 32 is 4.
A class has 28 boys and 32 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 28 and 32. Hence, GCF of 28 and 32 is 4.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(28, 32) = ( 28 * 32 ) / LCM(28, 32) = 4.
What is the GCF of 28 and 32?GCF of 28 and 32 is 4.
Ram has 28 cans of Pepsi and 32 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 28 and 32. Hence GCF of 28 and 32 is 4. So the number of tables that can be arranged is 4.
Mary has 28 blue buttons and 32 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 28 and 32. Hence, the GCF of 28 and 32 or the greatest arrangement is 4.
Kamal is making identical balloon arrangements for a party. He has 28 maroon balloons, and 32 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 28 and 32. So the GCF of 28 and 32 is 4.
Kunal is making baskets full of nuts and dried fruits. He has 28 bags of nuts and 32 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 28 and 32. So the GCF of 28 and 32 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 28 bus tickets and 32 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 28 and 32. Hence, GCF of 28 and 32 is 4.