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Mashutka [201]
3 years ago
10

Given three different prime numbers

title="p_1 \ \ ; \ \ p_2" alt="p_1 \ \ ; \ \ p_2" align="absmiddle" class="latex-formula"> and p_3 satisfy equation p_1+p_2+p_3=202 . Find the maximum value of
\pmb {p_1 \times p_2\times p_3=?}
Mathematics
1 answer:
Stels [109]3 years ago
8 0

Answer:

  • 19982

Step-by-step explanation:

As we know all primes but 2 are odd numbers.

It means sum of any 3 primes not including 2 is odd.

Since we have sum of 202, one of our primes is 2.

Sum of the other two primes is 200.

In order to have maximum value of p*(200 - p) these two numbers must be closer to each other. So we are looking for two primes around 100.

<u>We can test all primes less than 200:</u>

  • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199

<u>The 3 primes with max product are:</u>

  • 2, 97, 103

<u>The value is:</u>

  • 2*97*103 = 19982
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