show that the set of all factors of 12 under divisibility forms a lattice. Please answer!!!!!
Answers
Answer:1,2,3,4,6,12
Step-by-step explanation:
Answer:
Therefore, the set of all factors of 12 under divisibility forms a lattice {1, 2, 3, 4, 6, 12}.
Step-by-step explanation:
Given that the number is 12.
We will divide all the number starting from 1 to 12.
So we get the results as follows:
12/1 = 12
12/2 = 6
12/3 = 4
12/4 = 3
12/5 = 2,4
12/6 = 2
12/7 = 1.71
12/8 = 1.5
12/9 = 1.33
12/10 = 1.2
12/11 = 1.09
12/12 = 1
For the aforementioned, filter out the positive integer quotient while rejecting the decimals.
The factors of 12 are 1, 2, 3, 4, 6, 12.
These are numbers that when multiplied with each other results in 12.So here are the factor pairs of 12 are:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
4 x 3 = 12
6 x 2 = 12
12 x 1 = 12
Hence, the set of all factors of 12 under divisibility forms a lattice {1, 2, 3, 4, 6, 12}.
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