Math Problem Statement
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:
- The prime numbers between 1 and 999,999 include 2, 3, 5, and 7, among others.
- Notice that the product of any number with 5 and an even number (such as 2) will end in 0 because , 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:
- What is the significance of the unit digit in mathematical problems?
- How do unit digits affect multiplication results?
- Why does the presence of both 2 and 5 ensure a unit digit of 0?
- Are there other combinations of numbers that result in a unit digit of 0?
- 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