Math Problem Statement

Banyak faktor positif dari bilangan empat angka tersebut adalah ....

Solution

The question in the image asks about the number of positive divisors (factors) of a four-digit number, but the specific number is not provided in the visible part of the image. Since the available answers are:

  • A. 6
  • B. 12
  • C. 18
  • D. 24
  • E. 36

Without knowing the exact number in question, I can't calculate its exact number of divisors.

To solve a problem like this generally:

  1. You need to find the prime factorization of the given number.
  2. Once you have the prime factorization n=p1e1×p2e2××pkekn = p_1^{e_1} \times p_2^{e_2} \times \dots \times p_k^{e_k}, the formula to calculate the number of divisors is: Number of divisors=(e1+1)(e2+1)(ek+1)\text{Number of divisors} = (e_1 + 1)(e_2 + 1) \dots (e_k + 1) Where p1,p2,,pkp_1, p_2, \dots, p_k are the prime factors and e1,e2,,eke_1, e_2, \dots, e_k are their respective exponents.

Would you like to share more information on the number mentioned, or have any other questions related to this problem?

Here are five related questions you might find useful:

  1. What is prime factorization, and how is it useful in finding divisors?
  2. How do we efficiently find divisors for very large numbers?
  3. What are the properties of numbers with exactly 6, 12, or 24 divisors?
  4. How does the number of divisors change if a number has repeated prime factors?
  5. Why is the formula for calculating divisors dependent on the exponents in prime factorization?

Tip: Always check the prime factorization of a number first when asked to find its divisors; this simplifies the problem considerably.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Number Theory
Divisibility
Prime Factorization

Formulas

Number of divisors = (e1 + 1)(e2 + 1)...(ek + 1) where n = p1^e1 * p2^e2 * ... * pk^ek

Theorems

Divisor Counting Formula

Suitable Grade Level

Grades 9-12