The problem states that the number has only two prime factors and is 100 times the number of its factors.

Let's denote the two prime factors as p and q. Since the number has only two prime factors, the number can be written in the form of p^a * q^b, where a and b are positive integers.

The number of factors of a number in the form of p^a * q^b is (a+1)(b+1).

According to the problem, p^a * q^b = 100 * (a+1)(b+1).

The least such number would be when a = b = 1, which gives us p*q = 100*4 = 400.

The only two prime numbers that multiply to 400 are 2 and 5.

So, the least number satisfying these conditions is 2^2 * 5^2 = 100.

The sum of the digits of this number is 1 + 0 + 0 = 1.

Question

The problem states that the number has only two prime factors and is 100 times the number of its factors.

Let's denote the two prime factors as p and q. Since the number has only two prime factors, the number can be written in the form of p^a * q^b, where a and b are positive integers.

The number of factors of a number in the form of p^a * q^b is (a+1)(b+1).

According to the problem, p^a * q^b = 100 * (a+1)(b+1).

The least such number would be when a = b = 1, which gives us p*q = 100*4 = 400.

The only two prime numbers that multiply to 400 are 2 and 5.

So, the least number satisfying these conditions is 2^2 * 5^2 = 100.

The sum of the digits of this number is 1 + 0 + 0 = 1.

Knowee AI · Accepted Answer

The problem states that the number has only two prime factors and is 100 times the number of its factors.

Let's denote the two prime factors as p and q. Since the number has only two prime factors, the number can be written in the form of p^a * q^b, where a and b are positive integers.

The number of factors of a number in the form of p^a * q^b is (a+1)(b+1).

According to the problem, p^a * q^b = 100 * (a+1)(b+1).

The least such number would be when a = b = 1, which gives us p*q = 100*4 = 400.

The only two prime numbers that multiply to 400 are 2 and 5.

So, the least number satisfying these conditions is 2^2 * 5^2 = 100.

The sum of the digits of this number is 1 + 0 + 0 = 1.

A natural number has only two prime factors. It is 100 times the number of its factors. Find the sum of the digits of the least number satisfying these conditions.1432

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