answer:
To determine the largest prime number that divides evenly into the sum of 1 + 2 + 3 + ... + 78, we can calculate the sum of these numbers and then find the largest prime factor of that sum.
The sum of an arithmetic series can be calculated using the formula:
Sum = (n/2)(first term + last term)
In this case, the first term is 1 and the last term is 78, so we have:
Sum = (78/2)(1 + 78) = 39 * 79 = 3081
Now, we need to find the largest prime factor of 3081. We can use prime factorization or a calculator to determine this.
Using prime factorization:
Prime factorization of 3081: 3 * 7 * 7 * 19
The largest prime factor is 19.
Therefore, the largest prime number that divides evenly into the sum 1 + 2 + 3 + ... + 78 is 19.
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