Math Problem Statement

Find the unit digit of the product of all the prime numbers between 1 and 999999.

Solution

The question in the image asks:

"Find the unit digit of the product of all the prime numbers between 1 and 999999."

To solve this, let’s analyze the prime numbers within the range given:

  1. The prime numbers between 1 and 999,999 include 2, 3, 5, and 7, among others.
  2. Notice that the product of any number with 5 and an even number (such as 2) will end in 0 because 2×5=102 \times 5 = 10, which has a unit digit of 0.

Since 2 and 5 are among the prime numbers within this range, their product (and thus the product of all primes in this range) will end in 0.

Answer: The unit digit of the product is 0.

Would you like further explanation or have any questions?

Here are some related questions you might find interesting:

  1. What is the significance of the unit digit in mathematical problems?
  2. How do unit digits affect multiplication results?
  3. Why does the presence of both 2 and 5 ensure a unit digit of 0?
  4. Are there other combinations of numbers that result in a unit digit of 0?
  5. How can we generalize this method for other ranges of prime numbers?

Tip: When determining the unit digit of a product, look for combinations like 2 and 5, as their product guarantees a 0 in the unit place.

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Math Problem Analysis

Mathematical Concepts

Prime Numbers
Unit Digit
Multiplication

Formulas

Unit digit of the product of numbers involving 2 and 5 results in 0

Theorems

Properties of unit digits in multiplication involving primes

Suitable Grade Level

Grades 9-12