Last two digits of a power

MediumCombinatorics Brainteasers~5m

What are the last two digits of $2^{100}$ ? (Give the two-digit number, e.g. an answer of $\ldots07$ would be $7$ .)

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Euler needs $\gcd(a,m)=1$ ; here $\gcd(2,100)=2$ , so split $100=4\times 25$ .
Mod $4$ it's $0$ ; mod $25$ use $\phi(25)=20$ ; then recombine with CRT.

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