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2 years ago

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The number 26411 is completely divisible by

2 answers:

professor190 [17]2 years ago

7 0

Answer:

7, you can just your calculator to test it out.

Yanka [14]2 years ago

5 0

Answer:

Step-by-step explanation:

Where to start?

It isn't 2 and it isn't 3. You tell it's not 2 because it is an odd number.

It isn't 3 because the digits (26411 = 2 + 6 + 4 + 1 + 1) add up to 14 which is not divisible by 3, so the whole number is not divisible by 3.

It is not divisible by 5 because numbers divisible by 5 end either in 0 (which would make it even and divisible by 2) or 5. This one doesn't end in 5.

The very first number you can try is 7. That works. 3773 is the result.

The next prime to try is 11. I have a feeling that will work as well. Let's try it. It works as well. It's the symmetry of 3773 that made me look at eleven. There is a very complicated rule having to do with the odd and even places subtracted that tells you whether a number is divisible by 11 or not.

343 is the resulting number. I think that is 7^3 which is correct. So here's your answer

7 * 7 *7 * 7 * 11 is the answer. It's worthwhile to know how to do this. Factoring large numbers is one of the cornerstones of mathematics. Computers love this kind of thing.

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Can someone give me the answers and step by step instructions please??

professor190 [17]

Answer:

$-1,4,-7,10,...$ neither

$192,24,3,\frac{3}{8},...$ geometric progression

$-25,-18,-11,-4,...$ arithmetic progression

Step-by-step explanation:

Given:

sequences: $-1,4,-7,10,...$

$192,24,3,\frac{3}{8},...$

$-25,-18,-11,-4,...$

To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For $-1,4,-7,10,...$ :

$4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)$

Hence,the given sequence does not form an arithmetic progression.

$\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}$

Hence,the given sequence does not form a geometric progression.

So, $-1,4,-7,10,...$ is neither an arithmetic progression nor a geometric progression.

For $192,24,3,\frac{3}{8},...$ :

$\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}$

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For $-25,-18,-11,-4,...$ :

$-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)$

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

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