625 + 626 + 627 + 628 is divisible by:

The correct answer is 259.

The question asks about the expression $6^{25}+6^{26}+6^{27}+6^{28}$, which is divisible by one of the given options.

Step 1: Factor out the smallest power of 6

Notice that every term shares a common factor of $6^{25}$. We factor it out:

$6^{25}+6^{26}+6^{27}+6^{28}=6^{25}(6^0+6^1+6^2+6^3)$

Step 2: Evaluate the bracket

Calculate each power of 6 inside the parentheses:

$6^0=1$

$6^1=6$

$6^2=36$

$6^3=216$

Now add them:

$1+6+36+216=259$

Step 3: Write the final factored form

$6^{25}+6^{26}+6^{27}+6^{28}=6^{25}\times 259$

Step 4: Conclusion

Since the entire expression equals $6^{25}\times 259$, it is clearly divisible by 259. The factor 259 divides the expression exactly, with no remainder.

Among all the options — 256, 254, 255, and 259 — only 259 appears directly as a factor of the expression.