What are the rightmost four digits of the binary equivalent of the decimal number 4739685

Question

What are the rightmost four digits of the binary equivalent of the decimal number 4739685

My approach–

I converted the whole number into its binary equivalent and then checked out the last 4 digits, is there any shorter way to find it directly, I was thinking as in the case of finding last 4 digits in base 10 we do mod 10^4, so is there anything like 2^4 that we can do to find the last 4 digits in this case ? like 4739685 mod 16 ?

Answer 1

Last 4 digits of binary = Last hex-digit of hexadecimal

$10^4 \pmod{16} ≡ 2^4×5^4 \pmod{2^4} ≡ 0$

$4739685 \pmod{16} ≡ 9685-10000 \pmod{16} ≡ -315+320 \pmod{16} ≡ 5$

hex-digit of 5 = binary of 0101