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. 88 and 132 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 88 and also of 132.
- Every number is a factor of zero (0), since 88 x 0 = 0 and 132 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, 22, 44, 88 are exact divisors of 88 and 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 are exact divisors of 132.
- Factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88. Each factor divides 88 without leaving a remainder.
Simlarly, factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. Each factor divides 132 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 11, 22, 44, 88 are all less than or equal to 88 and 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 are all less than or equal to 132.
Steps to find Factors of 88 and 132
- Step 1. Find all the numbers that would divide 88 and 132 without leaving any remainder. Starting with the number 1 upto 44 (half of 88) and 1 upto 66 (half of 132). The number 1 and the number itself are always factors of the given number.
88 ÷ 1 : Remainder = 0
132 ÷ 1 : Remainder = 0
88 ÷ 2 : Remainder = 0
132 ÷ 2 : Remainder = 0
88 ÷ 4 : Remainder = 0
132 ÷ 3 : Remainder = 0
88 ÷ 8 : Remainder = 0
132 ÷ 4 : Remainder = 0
88 ÷ 11 : Remainder = 0
132 ÷ 6 : Remainder = 0
88 ÷ 22 : Remainder = 0
132 ÷ 11 : Remainder = 0
88 ÷ 44 : Remainder = 0
132 ÷ 12 : Remainder = 0
88 ÷ 88 : Remainder = 0
132 ÷ 22 : Remainder = 0
132 ÷ 132 : Remainder = 0
Hence, Factors of
88 are 1, 2, 4, 8, 11, 22, 44, and 88
And, Factors of
132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132
Examples of GCF
Sammy baked 88 chocolate cookies and 132 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 88 and 132.
GCF of 88 and 132 is 44.
A class has 88 boys and 132 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 88 and 132. Hence, GCF of 88 and 132 is 44.
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(88, 132) = ( 88 * 132 ) / LCM(88, 132) = 44.
What is the GCF of 88 and 132?GCF of 88 and 132 is 44.
Ariel is making ready to eat meals to share with friends. She has 88 bottles of water and 132 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 88 and 132. So the GCF of 88 and 132 is 44.
Mary has 88 blue buttons and 132 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 88 and 132. Hence, the GCF of 88 and 132 or the greatest arrangement is 44.
Kamal is making identical balloon arrangements for a party. He has 88 maroon balloons, and 132 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 88 and 132. So the GCF of 88 and 132 is 44.
Kunal is making baskets full of nuts and dried fruits. He has 88 bags of nuts and 132 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 88 and 132. So the GCF of 88 and 132 is 44.