Find a number greater than 25 that has more factors than the number 19, 21, 23 and 25

2 answers:

6 0

19 has 2 factors (1,19)
21 has 4 factors (1,3,7,21)
23 has 2 factors (1,23)
25 has 3 factors (1,5,25)
you need the nearest number 25 that has 5 factors or more :28(1,2,4,7,14,28)

-BARSIC- [3]3 years ago

4 0

Answer:

The possible number is 28.

Step-by-step explanation:

Since,

Factors of 19 = 1, 19,

Factors of 21 = 1, 3, 7, 21,

Factors of 23 = 1, 23,

Factors of 25 = 1, 5, 25

Now, numbers greater than 25 are,

26, 27, 28, 29, ......

Factors of 26 = 1, 2, 13, 26,

Factors of 27 = 1, 3, 9, 27,

Factors of 28 = 1, 2, 4, 7, 14, 28

Hence, a number greater than 25 that has more factors than the number 19, 21, 23 and 25 would be 28.

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√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q.

frutty [35]

Answer:

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

$\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\$