Question

How many positive factors does

62x(63^3+63^2+63+1)+1 have?

(With explanatio pls... Tnx)

Answer 1

63^3+63^2+63+1 = (63^4-1)/(63-1) = 63^4-1

So, your number is

63^4-1+1 = 63^4 = 3^8 * 7^4

So, the prime factors are 3 and 7

I'll leave it to you to determine how many factors there are in all

Answer 2

Tnx... But where did exponent 4 and minus one come from?

Answer 3

[AI-generated answer — Explain Bot]

To find the number of positive factors of the given expression, we can factorize it and then count the factors.

Let's break down the expression inside the parentheses:
63^3 + 63^2 + 63 + 1

To simplify, we start by factoring out 63 from each term:

63^3 + 63^2 + 63 + 1 becomes 63(63^2 + 63 + 1) + 1

Now, we can see that 63 is a factor common to each term inside the parentheses. We can factor it out:

63(63^2 + 63 + 1) + 1 becomes 63(1 + 63 + 63^2) + 1

Now, let's simplify the expression:

63(1 + 63 + 63^2) + 1
= 63(1 + 63 + 3969) + 1
= 63(4033) + 1
= 254079 + 1
= 254080

Now, we have the simplified expression: 62x(254080) + 1.

To find the number of positive factors, we need to factorize the expression further and then count the factors.

The expression 62x(254080) + 1 can be factored as:

62(2^1)x(5^1)x(47^1)x(271^1) + 1

The exponents represent the power to which each prime factor is raised.

To calculate the number of factors, we add 1 to each exponent and multiply them together.

For this expression:
Power of 2 = 1 + 1 = 2
Power of 5 = 1 + 1 = 2
Power of 47 = 1 + 1 = 2
Power of 271 = 1 + 1 = 2

Now, multiply the exponents together:

2 x 2 x 2 x 2 = 16

So, the given expression 62x(63^3+63^2+63+1)+1 has 16 positive factors.