Let n be the product of the two smallest 3-digit prime numbers. Find the sum of the digits of n.
Answer (2)
To solve the problem, we need to follow these steps:
Identify the Smallest 3-Digit Prime Numbers:
The two smallest prime numbers that are 3-digit are 101 and 103. A prime number is one that has no divisors other than 1 and itself.
Calculate the Product of These Prime Numbers:
n = 101 × 103
To find this product, use the distributive property (also known as the FOIL method for two binomials) or directly multiply:
Multiply: 101 by 103: 101 × 103 = ( 100 + 1 ) ( 100 + 3 )
Expand: = 100 × 100 + 100 × 3 + 1 × 100 + 1 × 3
Calculate: = 10000 + 300 + 100 + 3
Add these numbers together: = 10403
Find the Sum of the Digits of n :
Now that we know n = 10403 , we add the digits:
1 + 0 + 4 + 0 + 3 = 8
Thus, the sum of the digits of n is 8.
The sum of the digits of the product of the two smallest 3-digit prime numbers (101 and 103) is 8. This product is calculated as 10403, and the digits are summed to achieve this result.
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