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The last two digits of seven to the power 2024

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What are the last two digits of 7 to the power 2024?

The number itself has about 1,700 digits, so you must find a shortcut. Explain the method in a way that would also settle the last two digits of 7 to the power of any other exponent, and say why the last two digits of a product depend only on the last two digits of the factors.

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The last two digits of a product depend only on the last two digits of the factors. Compute the last two digits of 7, 7 squared, 7 cubed, 7 to the fourth, and look for a repeat.

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