HOD(504;414)=

It seems you’re asking for the highest common divisor (GCD/HCF) of 504 and 414.

Using the Euclidean algorithm:

• 504 = 414 + 90
• 414 = 4×90 + 54
• 90 = 1×54 + 36
• 54 = 1×36 + 18
• 36 = 2×18 + 0

GCD(504, 414) = 18.

So, HOD(504;414) = 18. (If you meant something else by HOD, please clarify.)