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
ivanzaharov [21]
3 years ago
6

Find the smallest positive integer n such that n(n+1)(n+2) is divisible by 247.

Mathematics
1 answer:
Butoxors [25]3 years ago
5 0

Answer:

37 is the smallest positive integer n such that n(n+1)(n+2) is divisible by 247.

Step-by-step explanation:

First we will find the prime factors of 247:

247 = 13 x 19 (which are both prime).

So now we need to find a number (the smallest one) that is of the form (n)(n+1)(n+2) (the product of three consecutive numbers) and that is divisible by both 13 and 19 (and therefore divisible by 247)

Let's take a look at the multiples of 13: 13, 26, 39, 52...

Let's take a look at the multiples of 19: 19, 38, 57...

We can see that the first time we have two multiples close together are the 38 (for 19) and the 39 (for 17).

So, if our number has both 38 and 39 as factors, then it will be divisible by 247.

However, we need not two but three consecutive numbers, and since we want the number to be the smallest positive integer, we will add 37 (since our other choice would be to add 40 and that would make the number bigger) and thus our number is (37)(38)(39) or in other words (37)(37 + 1)(37 + 2) and therefore this is the smallest positive number such that n(n+1)(n+2) is divisible by 247.

You might be interested in
Solve step by step! Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!
Aliun [14]

For the 60°'s topmost line, you can find the angle next to it is 120° because it's a straight line. You can do the same for 95° if you put that the angle opposite it is equal already because it's the opposite angle, so you subtract from 180° again to get 85°. When you extend the lines, you can find the alternate interior angles to the 60° and 85°, which are congruent to them. You then get that for both the formed triangles there is one 85° and one 60°, which together with one more angle should equal 180°. Through knowing that the sun of the triangles angles should be 180°, if you subtract the sum of 60° and 85° from 180°, you get the angle of the 3rd angle in the triangles (35°). This angle also forms 180° with x on a line, so 180°-35°=x, which is 145° seemingly.

4 0
3 years ago
1 ton is equal to 2000 pounds.how many pounds are in 4 tons, 568 pounds?
LekaFEV [45]

Answer:

Hello There!!

Step-by-step explanation:

If 1 ton=2000 (1 ton to 4 is times by 4 so 2000

4 tons=8000 is times by 4)

hope this helps, have a great day!!

~Pinky~

6 0
3 years ago
Read 2 more answers
Helppppppppppppppppppppp I need this ASAP
Nataliya [291]

Answer:

Can you just not be so desperate please?

5 0
3 years ago
Read 2 more answers
Find the leg of each isosceles right triangle if<br> hypotenuse is 5 square root 6
Mekhanik [1.2K]
Let x be the measure of both legs since the given is an isosceles right triangle. By the Pythagorean theorem we calculate for the legs,
                                      x² + x² = (5 sqrt 6)²
The value of x from the given equation is approximately 8.66 units. 
7 0
3 years ago
Which represents all the values of x that make the rational expression 2x-4 over x-5 undefined?
mixas84 [53]

For this case we have the following expression:

\frac {2x-4} {x-5}

By definition, we have the expression undefined when the denominator is 0.

So:

x-5 = 0

Adding 5 to both sides of the equation:

x-5 + 5 = 5\\x = 5

Thus, the expression is undefined when x = 5.

Answer:

Option B

5 0
3 years ago
Other questions:
  • Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows t
    13·1 answer
  • The two right triangles shown above have equal perimeters. The hypotenuse of the orange triangle is one leg of the green triangl
    6·1 answer
  • (2x+2) what is the value of x?​
    9·1 answer
  • HURRY PLS HELPP !!!
    8·2 answers
  • The equations x minus 2 y = 4, 4 x + 5 y = 8, 6 x - 5 y = 15, and x + 2 y = 0 are shown on the graph below. On a coordinate plan
    7·2 answers
  • What is the solution to this inequality x-7&lt;1
    8·2 answers
  • A little help would be nice pls and thku
    15·1 answer
  • 9x/2&lt;=6(x-3)+3x<br> solve using that method in picture! <br><br> helppppp <br> please. ASAP
    14·1 answer
  • use the model to create zero pairs.What is an equivalent expression that has two terms? 2x +(-x) +3 +(-2)
    12·1 answer
  • Answer fast plsssssss
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!