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. 496 and 1116 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 496 and also of 1116.
- Every number is a factor of zero (0), since 496 x 0 = 0 and 1116 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, 16, 31, 62, 124, 248, 496 are exact divisors of 496 and 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116 are exact divisors of 1116.
- Factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496. Each factor divides 496 without leaving a remainder.
Simlarly, factors of 1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116. Each factor divides 1116 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 are all less than or equal to 496 and 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116 are all less than or equal to 1116.
Steps to find Factors of 496 and 1116
- Step 1. Find all the numbers that would divide 496 and 1116 without leaving any remainder. Starting with the number 1 upto 248 (half of 496) and 1 upto 558 (half of 1116). The number 1 and the number itself are always factors of the given number.
496 ÷ 1 : Remainder = 0
1116 ÷ 1 : Remainder = 0
496 ÷ 2 : Remainder = 0
1116 ÷ 2 : Remainder = 0
496 ÷ 4 : Remainder = 0
1116 ÷ 3 : Remainder = 0
496 ÷ 8 : Remainder = 0
1116 ÷ 4 : Remainder = 0
496 ÷ 16 : Remainder = 0
1116 ÷ 6 : Remainder = 0
496 ÷ 31 : Remainder = 0
1116 ÷ 9 : Remainder = 0
496 ÷ 62 : Remainder = 0
1116 ÷ 12 : Remainder = 0
496 ÷ 124 : Remainder = 0
1116 ÷ 18 : Remainder = 0
496 ÷ 248 : Remainder = 0
1116 ÷ 31 : Remainder = 0
496 ÷ 496 : Remainder = 0
1116 ÷ 36 : Remainder = 0
1116 ÷ 62 : Remainder = 0
1116 ÷ 93 : Remainder = 0
1116 ÷ 124 : Remainder = 0
1116 ÷ 186 : Remainder = 0
1116 ÷ 279 : Remainder = 0
1116 ÷ 372 : Remainder = 0
1116 ÷ 558 : Remainder = 0
1116 ÷ 1116 : Remainder = 0
Hence, Factors of
496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, and 496
And, Factors of
1116 are 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, and 1116
Examples of GCF
Sammy baked 496 chocolate cookies and 1116 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 496 and 1116.
GCF of 496 and 1116 is 124.
A class has 496 boys and 1116 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 496 and 1116. Hence, GCF of 496 and 1116 is 124.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(496, 1116) = ( 496 * 1116 ) / LCM(496, 1116) = 124.
What is the GCF of 496 and 1116?GCF of 496 and 1116 is 124.
Ram has 496 cans of Pepsi and 1116 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 496 and 1116. Hence GCF of 496 and 1116 is 124. So the number of tables that can be arranged is 124.
Mary has 496 blue buttons and 1116 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 496 and 1116. Hence, the GCF of 496 and 1116 or the greatest arrangement is 124.
Kamal is making identical balloon arrangements for a party. He has 496 maroon balloons, and 1116 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 496 and 1116. So the GCF of 496 and 1116 is 124.
Kunal is making baskets full of nuts and dried fruits. He has 496 bags of nuts and 1116 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 496 and 1116. So the GCF of 496 and 1116 is 124.
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 496 bus tickets and 1116 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 496 and 1116. Hence, GCF of 496 and 1116 is 124.