# Lesson: Counting the Divisors of Large Numbers

## Comment on Counting the Divisors of Large Numbers

### Great video! I am confused on

Great video! I am confused on the primes you ended up with. 1400 can be broken down to 100 and 14. Then 14 is simply factored to 7 and 2. 100 can be broken down to 10 and 10. Both of these 10's are individually factored to two sets of 5 and 2. So in total, I have three 2's, two 5's, and one 7. May you please explain how you got 2^4 and 5^2? Thank you in advance.

### Hi T J. Your prime

Hi T J. Your prime factorization of 1400 is correct. However, in the video, we find the prime factorization of 14,000﻿

### I don't understand why we

I don't understand why we count 0 so instead of counting 2 four times we count it five times!

### All factors of 720 will be in

All factors of 720 will be in the form (2^a)(3^b)(5^c)
Notice that, when a = 0, b = 0 and c = 0, we get (2^0)(3^0)(5^0) as a factor.

(2^0)(3^0)(5^0) = (1)(1)(1) = 1, and 1 is definitely a factor of 720.

Likewise, (2^0)(3^1)(5^1) = (1)(3)(5) = 15, and 15 is also a factor of 720

So, we need to consider the possibility of the exponents equaling 0.

Does that help?

Cheers,
Brent

This is a follow-up to the question you asked me (via email) about statement A.

First note that the question asks "Which of the following statements individually provide(s) sufﬁcient additional information to determine whether the slope of line k is negative?"

So, we need to determine whether the information in statement A is enough to be certain that the line's slope is negative.

STATEMENT A: The x-intercept of line k is twice the y-intercept of line k.

If the line's x-intercept is twice the y-intercept, then the line's slope MUST be negative. Here's why.

Let's say the line's y-intercept is k. This means the line passes through the y-axis at the point (0, k)

This means, the line's x-intercept is 2k (since the line's x-intercept is twice the y-intercept). This means the line passes through the x-axis at the point (2k, 0)

Now apply the slope formula to determine the slope of the line that passes through (0, k) and (2k, 0).

We get: Slope = (0 - k)/(2k - 0) = -k/2k = -1/2

Since the slope is definitely negative (for all values of k), we can conclude that statement A is true.

Does that help?

Cheers,
Brent

### Yes it helps! Thanks Brent.

Yes it helps! Thanks Brent.

### How do we find the prime

How do we find the prime factorisation of large numbers

### You won't be required to find

You won't be required to find the prime factorization of super huge numbers. In most cases, the number will be under 1000, and if it's bigger than 1000, it won't be complicated.

Cheers,
Brent

### Hi, thanks a lot for this

Hi, thanks a lot for this video, I am so happy to have learned it in this way!

### Thanks Carla. I'm glad you

Thanks Carla. I'm glad you like it!

### Dear Brent,

Dear Brent,
Appreciated for this solution
Works well.

### can we use this technique to

can we use this technique to find smaller values as well?

### Good question. Yes, the

Good question. Yes, the technique works for all numbers.