1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Reptile [31]
2 years ago
6

A certain positive integer has exactly 20 positive divisors. What is the smallest number of primes that could divide the integer

Mathematics
1 answer:
Alika [10]2 years ago
8 0

As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.

Note that  2,3,5 and 7   are the smallest primes, then use the reasoning from

(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.

But no such integers  k, l, m, and n  exist such that (k + 1)(l + 1)(m + 1) (n + 1)  = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors

Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents,  that, when 1 is added to each and all are multiplied together, would equal 20.  Put another way, we are looking for k, l and m ≥ 1   such that (k + 1)(l + 1)(m + 1) = 20

Note that the  only possibility here  is when we have 2 *2 *5  = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) =  2^4 * 3 * 5 = 240

Now......the only remaining possibility is  that this number is composed of the two smallest primes, 2 and 3,  and we are looking for  some k  and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities  are when k = 4 and l = 5, or vice-versa

So this number would factor as either 2^3 * 3^4   = 648  or 2^4 * 3^3 = 432 and both are > 240.

Learn more about positive integers at

brainly.com/question/1367050

#SPJ4

You might be interested in
What is the domain of the function y=tan (x/8)<br> Please Help<br> 15 Points
7nadin3 [17]

1. You have the function y=tan(\frac{x}{8} )

2. You know that y=\frac{sinx}{cosx} with cosx\neq 0, because the division by zero is not defined. So , cosx=0 for \frac{(2n+1)\pi}{2} where n is a integer number.

3. Then, to find the domain of the function given in the problem, you must make \frac{x}{8} \neq \frac{k\pi}{2}  \\ x\neq 4k\pi

Where k is odd number.

4. Therefore:

x\neq 4\pi (2n+1)

5. Finally, the domain is: 4\pi (2n+1)

The answer is: 4\pi (2n+1)

5 0
3 years ago
Read 2 more answers
the cost of 3 pints of ice cream is 7 dollars . what is the proportion used to find the cost ,c, of 9 pints of the same ice crea
AlekseyPX

Answer:

21

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Right triangle trigonometry scavenger hunt answers?
elena-s [515]

AnsAnswerwer:

sorry i can't help without the picture of the problem

Step-by-step explanation:

8 0
2 years ago
The cost of a cycle is $ 950 and that of a scooter is $ 23,500. He sold them together for $ 25,000. Find his profit. ​
e-lub [12.9K]

actual cost is 950+23,500=24450

he sold them for 25000 so his profit is 25000-950-23500=550

4 0
3 years ago
Read 2 more answers
1) 2 (x+3) +3 (5-x)=
Ugo [173]

Answer:

Below

Step-by-step explanation:

1. 2 (x+3) +3 (5-x)=

Simplifying

2(x + 3) + 3(5 + -1x) = 0

Reorder the terms:

2(3 + x) + 3(5 + -1x) = 0

(3 * 2 + x * 2) + 3(5 + -1x) = 0

(6 + 2x) + 3(5 + -1x) = 0

6 + 2x + (5 * 3 + -1x * 3) = 0

6 + 2x + (15 + -3x) = 0

Reorder the terms:

6 + 15 + 2x + -3x = 0

Combine like terms: 6 + 15 = 21

21 + 2x + -3x = 0

Combine like terms: 2x + -3x = -1x

21 + -1x = 0

Solving

21 + -1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21' to each side of the equation.

21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0

0 + -1x = 0 + -21

-1x = 0 + -21

Combine like terms: 0 + -21 = -21

-1x = -21

Divide each side by '-1'.

x = 21

Simplifying

x = 21

2.  3 (y+2) -4y=-24y

Simplifying

3(y + 2) + -4y = -24y

Reorder the terms:

3(2 + y) + -4y = -24y

(2 * 3 + y * 3) + -4y = -24y

(6 + 3y) + -4y = -24y

Combine like terms: 3y + -4y = -1y

6 + -1y = -24y

Solving

6 + -1y = -24y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '24y' to each side of the equation.

6 + -1y + 24y = -24y + 24y

Combine like terms: -1y + 24y = 23y

6 + 23y = -24y + 24y

Combine like terms: -24y + 24y = 0

6 + 23y = 0

Add '-6' to each side of the equation.

6 + -6 + 23y = 0 + -6

Combine like terms: 6 + -6 = 0

0 + 23y = 0 + -6

23y = 0 + -6

Combine like terms: 0 + -6 = -6

23y = -6

Divide each side by '23'.

y = -0.2608695652

Simplifying

y = -0.2608695652

3.  -(x+2) -2(1-x)=

Simplifying

-1(x + 2) + -2(1 + -1x) = 0

Reorder the terms:

-1(2 + x) + -2(1 + -1x) = 0

(2 * -1 + x * -1) + -2(1 + -1x) = 0

(-2 + -1x) + -2(1 + -1x) = 0

-2 + -1x + (1 * -2 + -1x * -2) = 0

-2 + -1x + (-2 + 2x) = 0

Reorder the terms:

-2 + -2 + -1x + 2x = 0

Combine like terms: -2 + -2 = -4

-4 + -1x + 2x = 0

Combine like terms: -1x + 2x = 1x

-4 + 1x = 0

Solving

-4 + 1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + 1x = 0 + 4

Combine like terms: -4 + 4 = 0

0 + 1x = 0 + 4

1x = 0 + 4

Combine like terms: 0 + 4 = 4

1x = 4

Divide each side by '1'.

x = 4

Simplifying

x = 4

4. whats ? is the equation

6 0
3 years ago
Other questions:
  • Help with just 3 please.
    15·1 answer
  • For a regular 15-gon:
    7·1 answer
  • Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviat
    14·1 answer
  • A cycling race is 17 miles long. The cyclists will begin at point S and ride a number of laps around a neighborhood block. After
    5·2 answers
  • a bottling machine can fill 300 bottles in 5 minutes at this rate how many bottles can be filled in 8 minutes
    7·2 answers
  • Can you shade the venn diagram by <br>(A intersection B)intersection C​
    10·1 answer
  • Suppose that a worker in Caninia can produce either 2 blankets or 8 meals per day, and a worker in Felinia can produce either 5
    14·1 answer
  • Which graph could represent the amount of green beans when selling at a unit rate of G dollars per pound?
    6·2 answers
  • On September 1, 2012, Ramos Inc. approved a plan to dispose of a segment of its
    5·1 answer
  • HELP i don’t know what the slope is or how to do this!!!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!