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Exercise Overview

This exercise demonstrates how to use loops to solve mathematical problems. We’ll create a program that finds and prints:
  • Prime numbers
  • Odd numbers
  • Multiples of 7
All within the range of 100 to 150.

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Problem Statement

Create a program that prints the following within the range of 100 to 150:

Prime Numbers

Numbers divisible only by 1 and themselves

Odd Numbers

Numbers not divisible by 2

Multiples of 7

Numbers divisible by 7

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Solution

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Finding Prime Numbers

To find prime numbers, we use a nested loop to check if a number has any divisors: 
//Números Primos
print('\nNúmeros Primos');
for (var i = 100; i <= 150; i++) {
  int contador = 0;
  for (var j = 2; j <= i - 1; j++) {
    if (i % j == 0){
      contador++;
    }
  }
  if (contador == 0){
    print('El Número $i es Primo');
  }
}
1

Iterate through the range

The outer loop goes from 100 to 150
2

Check for divisors

The inner loop tests if the number is divisible by any number from 2 to i-1
3

Count divisors

If we find a divisor, increment the counter
4

Determine if prime

If the counter is 0, the number has no divisors and is therefore prime

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Finding Odd Numbers

For odd numbers, we can start at 101 and increment by 2: 
//Números Impares
print('\nNúmeros Impares');
for (var i = 101; i < 150; i += 2) {
  print('Número Impar: $i');
}
By starting at 101 (an odd number) and incrementing by 2, we skip all even numbers automatically. This is much more efficient than checking each number.

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Finding Multiples of 7

For multiples of 7, we use the modulo operator: 
//Múltiplos de 7
print('\nNúmeros Múltiplos de 7');
for (var i = 100; i < 150; i++) {
  if (i % 7 == 0){
    print('Número Múltiplo de 7: $i');
  }
}
The modulo operator % returns the remainder of a division. If i % 7 == 0, it means i is perfectly divisible by 7.

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Complete Program

void main() {
  //Hacer un programa que imprima dentro del rango comprendido del 100 al 150 lo siguiente:
  //- Números primos 
  //- Números Impares 
  //- Múltiplos de 7

  //Números Primos
  print('\nNúmeros Primos');
  for (var i = 100; i <= 150; i++) {
    int contador = 0;
    for (var j = 2; j <= i - 1; j++) {
      if (i % j == 0){
        contador++;
      }
    }
    if (contador == 0){
      print('El Número $i es Primo');
    }
  }

  //Números Impares
  print('\nNúmeros Impares');
  for (var i = 101; i < 150; i += 2) {
    print('Número Impar: $i');
  }

  //Múltiplos de 7
  print('\nNúmeros Múltiplos de 7');
  for (var i = 100; i < 150; i++) {
    if (i % 7 == 0){
      print('Número Múltiplo de 7: $i');
        
    }
  }
}

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Key Concepts

For Loops

Used to iterate over a range of numbers

Nested Loops

A loop inside another loop, useful for complex algorithms

Modulo Operator

% returns the remainder of a division

Loop Optimization

Using i += 2 skips unnecessary iterations

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Practice Challenges

Modify the program to work with a range of 1 to 1000. What optimizations could you make to the prime number algorithm?
Add a section to print all even numbers in the range.
Add a section to print all perfect squares (4, 9, 16, 25, etc.) in the range.

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