A data processing apparatus and method of operating such a data processing apparatus are provided, for responding to a division instruction to perform a division operation to generate a result value by dividing an input numerator specified by the division instruction by an input denominator specified by the division instruction. The input numerator and input denominator are binary values. The apparatus comprises division circuitry configured to generate the result value by carrying out the division operation, power-of-two detection circuitry configured to signal a bypass condition if the input denominator has a value given by ±2N, where N is a positive integer, and bypass circuitry configured, in response to signalling of the bypass condition, to cause the division circuitry to be bypassed and to cause the result value to be generated as the input numerator shifted by N bits.