To find the last two digits of 6521786, we need to compute the value of $6521786 \mod 100$, which gives the remainder when 6521786 is divided by 100.

Step-by-step solution:

$6521786 \div 100 = 65217 \text{ remainder } 86$ So, the last two digits of 6521786 are 86.

However, none of the provided answer choices (71, 21, 01, 91) match 86. Could you verify if there was a typo in the options or if you're asking about a different number?

Would you like me to assist further in checking this or in providing an explanation for another problem?

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Here are some related questions you can explore:

1. How do you calculate the last two digits of large numbers without a calculator?
2. What is modular arithmetic, and how is it used in number theory?
3. How do you compute powers of numbers modulo 100 efficiently?
4. What is the concept of number remainders when dividing large numbers?
5. How would you solve for the last two digits of numbers in a different base?

Tip: When working with powers or large numbers and trying to find the last two digits, using modular arithmetic helps avoid dealing with the full number.