Answer:

Given,

The number divides 315 (320 – 5) and 450 (457 – 7).

∴ Required number = HCF (315, 450)

Apply Euclid’s algorithm,

315 ) 450 ( 1

– 315

____________

135 ) 315 ( 2

– 270

____________

45 ) 135 ( 3

– 135

____________

0

HCF of 315 and 450 is 45.

The number is 45.