why do 30 and 42 have the same number of positive divisors ?

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https://math.stackexchange.com › questions › 869396 › why-do-42-and-30-have-the-same-structure-in-the-diagramm-of-hasse
Why do 42 and 30 have the same structure in the diagramm of Hasse?
42 = 2 ⋅ 3 ⋅ 7 while 30 = 2 ⋅ 3 ⋅ 5 since the Hasse diagram ignores what the actual primes are these numbers have the same Hasse diagram. That is, the Hasse diagram only cares if the primes inside the product are different.

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If a is a positive divisor of both 30 and 42, then a is also a positiv
If a is a positive divisor of both 30 and 42, then a is also a positive divisor of which integer? I. -12 II. 12 …

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https://math.stackexchange.com › questions › 821718 › number-of-positive-divisors-of-a-number
Number of positive divisors of a number – Mathematics Stack Exchange
In other words, the positive divisors of a number come in pairs. That means all numbers have an even number of positive divisors unless k = n k. Because if k does equal n k, you discard one of them from your count. You don’t count the same thing twice.

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https://www.chegg.com › homework-help › discrete-mathematicians-especially-enjoy-counting-problems-p-chapter-1.3-problem-12e-solution-9781285402062-exc
Solved: Discrete mathematicians especially enjoy counting … – Chegg
i. 42 = 2 × 3 × 7. (Why do 30 and 42 have the same number of positive divisors?) j. 2310 = 2 × 3 × 5 × 7 × 11. k. 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8. l. 0. Step-by-step solution 100% (7 ratings) for this solution Step 1 of 3 The objective is to find the number of positive divisors of the following. (a) The number is 8. This can be written as:

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How many positive integer have exactly three proper divisors (positive …
because a divisor is the product of the same prime factors but its powers are equal or less than the original power in . Obviously, for a number with 3 proper positive integer divisors, there are 4 (not necessarily proper) divisors, and then the possible number of prime factors is 1 or 2. The prime decomposition should be or .

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https://www.quora.com › How-many-positive-integers-have-exactly-three-proper-divisors-each-of-which-is-less-than-30?share=1
How many positive integers have exactly three proper divisors … – Quora
Let me explain why that’s the case: Consider the number 2^n, where n is any positive integer. For any value of n that we choose, the number 2^n will have (n -1) unique factors, excluding 1 and itself. For example, if n = 5, then 2^n = 32. The number 32 has 4 unique factors, whi Continue Reading 3 Quora User

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Divisors of 30 – Mathstoon
Divisors of 30 Formula. The prime factorization of 30 is given below. 30 = 2 1 ×3 1 ×5 1 (i) By the number of divisors formula, we have that the number of divisors of 30 is =(1+1)(1+1)(1+1)=2×2×2=8. (ii) By the sum of divisors formula, we have that the sum of the divisors of 30 is $=dfrac{2^2-1}{2-1} times dfrac{3^2-1}{3-1}$ $times dfrac{5^2-1}{5-1}$

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SOLVED:3.12. Discrcte mathematicians especially enjoy counting problems …
well for a bunch of things about prime numbers. And we can basically this this uh pie, this prime pie which I will call it. Prime Pie basically says that how m…

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Divisors of 42 – Mathstoon
The prime factorization of 42 is given below. 42 = 21 × 31 ×71 (i) By the number of divisors formula, we have that the number of divisors of 42 is = (1+1) (1+1) (1+1)=2×2×2=8. (ii) By the sum of divisors formula, we have that the sum of the divisors of 42 is = 2 2 − 1 2 − 1 × 3 2 − 1 3 − 1 × 7 2 − 1 7 − 1 = 4 − 1 1 × 9 − 1 2 × 49 − 1 6

https://numbermaniacs.com › Divisors › What-are-the-divisors-of-42.html

https://numbermaniacs.com › Divisors › What-are-the-divisors-of-42.html
What are the divisors of 42? – Number Maniacs
The divisors of 42 are all the postive integers that you can divide into 42 and get another integer. In other words, 42 divided by any of its divisors should equal an integer. Here we have the list of all divisors of 42. 1, 2, 3, 6, 7, 14, 21, 42 It’s interesting to note that when you divide 42 by one of its divisors, the result is also a divisor.

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