Looping constructs while contd

Project euler 3

• Refer Here for problem
• Largest prime factor of a number
  • it has to be a factor
  • it has to be a prime
  • it has to be a largest possible
• Example

70 =>
   factors: 2,5,7,10,14,35
   prime: 2,5,7
   largest: 7

27 =>
   factors: 3,9
   prime: 3
   largest: 3

• Solution for prime number

Hi Chaitra,
number = 7
is_prime = True
index = 2
while index < number
   if number%index == 0
      is_prime = False
      break
   index = index + 1

• Python

number = 13195
factor = number // 2
while factor > 1:
    # check if it is factor
    if number % factor == 0:
        # if factor also check if index it is prime
        is_prime = True
        index = 2
        while index <= factor//2 :
            if factor % index == 0:
                is_prime = False
                break
            index = index + 1
        if is_prime:
            print(factor)
            break
    factor = factor - 1

Project euler 5

• Refer Here
• Python

# Smallest multiple
number = 20

# boundary
index = 1
factorial = 1
while index <= number:
    factorial = factorial * index
    index += 1

max = factorial
index = number
while index <= factorial:
    # check if is divisible by all numbers from 2 to number
    divisible = True
    number_index = 2
    while number_index <= number:
        if index % number_index != 0:
            divisible = False
            break
        number_index += 1
    if divisible:
        print(index)
        break
    index += number

Project euler 6: Sum square difference

• Refer Here

# Project euler problem 6

number = 100

sum = (number * (number + 1)) // 2

square_sum = sum ** 2

square_number = 0
index = 1
while index <= number:
    square_number += index ** 2
    index += 1
print(square_sum - square_number)