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
- Every factor of a number is an exact divisor of that number, example 1, 7, 17, 49, 119, 289, 833, 2023, 14161 are exact divisors of 14161 and 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220, 242, 275, 484, 550, 605, 1100, 1210, 2420, 3025, 6050, 12100 are exact divisors of 12100.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 14161 and 12100 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 14161 and also of 12100.
Steps to find Factors of 14161 and 12100
- Step 1. Find all the numbers that would divide 14161 and 12100 without leaving any remainder. Starting with the number 1 upto 7080 (half of 14161) and 1 upto 6050 (half of 12100). The number 1 and the number itself are always factors of the given number.
14161 ÷ 1 : Remainder = 0
12100 ÷ 1 : Remainder = 0
14161 ÷ 7 : Remainder = 0
12100 ÷ 2 : Remainder = 0
14161 ÷ 17 : Remainder = 0
12100 ÷ 4 : Remainder = 0
14161 ÷ 49 : Remainder = 0
12100 ÷ 5 : Remainder = 0
14161 ÷ 119 : Remainder = 0
12100 ÷ 10 : Remainder = 0
14161 ÷ 289 : Remainder = 0
12100 ÷ 11 : Remainder = 0
14161 ÷ 833 : Remainder = 0
12100 ÷ 20 : Remainder = 0
14161 ÷ 2023 : Remainder = 0
12100 ÷ 22 : Remainder = 0
14161 ÷ 14161 : Remainder = 0
12100 ÷ 25 : Remainder = 0
12100 ÷ 44 : Remainder = 0
12100 ÷ 50 : Remainder = 0
12100 ÷ 55 : Remainder = 0
12100 ÷ 100 : Remainder = 0
12100 ÷ 110 : Remainder = 0
12100 ÷ 121 : Remainder = 0
12100 ÷ 220 : Remainder = 0
12100 ÷ 242 : Remainder = 0
12100 ÷ 275 : Remainder = 0
12100 ÷ 484 : Remainder = 0
12100 ÷ 550 : Remainder = 0
12100 ÷ 605 : Remainder = 0
12100 ÷ 1100 : Remainder = 0
12100 ÷ 1210 : Remainder = 0
12100 ÷ 2420 : Remainder = 0
12100 ÷ 3025 : Remainder = 0
12100 ÷ 6050 : Remainder = 0
12100 ÷ 12100 : Remainder = 0
Hence, Factors of
14161 are 1, 7, 17, 49, 119, 289, 833, 2023, and 14161
And, Factors of
12100 are 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220, 242, 275, 484, 550, 605, 1100, 1210, 2420, 3025, 6050, and 12100
Examples of GCF
Sammy baked 14161 chocolate cookies and 12100 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 14161 and 12100.
GCF of 14161 and 12100 is 1.
A class has 14161 boys and 12100 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 14161 and 12100. Hence, GCF of 14161 and 12100 is 1.
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(14161, 12100) = ( 14161 * 12100 ) / LCM(14161, 12100) = 1.
What is the GCF of 14161 and 12100?GCF of 14161 and 12100 is 1.
Mary has 14161 blue buttons and 12100 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 14161 and 12100. Hence, the GCF of 14161 and 12100 or the greatest arrangement is 1.
Kamal is making identical balloon arrangements for a party. He has 14161 maroon balloons, and 12100 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 14161 and 12100. So the GCF of 14161 and 12100 is 1.
Kunal is making baskets full of nuts and dried fruits. He has 14161 bags of nuts and 12100 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 14161 and 12100. So the GCF of 14161 and 12100 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 14161 bus tickets and 12100 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 14161 and 12100. Hence, GCF of 14161 and 12100 is 1.