In Windows 10, will the same online digital entitlement work for both 32 and 64 bit installations of the same version on the same PC?

My next door neighbour asked me to look at his laptop as it stopped working. He says it uses Windows 10, but he doesn't know whether it is a 32-bit or 64-bit version.

I have identified the problem is due to the death of the hard drive. he has never made any backups, so when I install a new drive it will be followed by a full clean install if Windows 10. I have established by running a Live DVD version of 64-bit Linux that the CPU is a 64 type.

I plan to download Windows 10 onto a DVD-RW media and install from the DVD. DVD-RW media do not have the capacity to download both 32 and 64 bit versions on to the same disk. So I will try one and if fails to activate I will try a re-installation of the other one. If the same entitlement will work for both, then I can just choose one of them and go with that.

I doubt whether my neighbour will worry about which version he has. Does anyone have any recommendation as to which one to use if either will work? From what I can find out, 64 bit might be slightly faster, but will preclude the possibility of running any 16 bit applications should he have any.

Any information about whether the same entitlement works for both 32 and 64 bit will be appreciated. Thank you.