Methods and apparatus to determine a remainder value are disclosed. A disclosed example method involves, during a compilation phase, causing a processor to multiply a dividend value by a first value to generate a second value associated with a product. The first value is associated with a scaled approximate reciprocal of a divisor value, and the scaled approximate reciprocal of the divisor value is determined using a compound exponent value. During a runtime phase, the processor is caused to multiply a third value from the second value. The third value is generated using at least a subset bitfield of the second value. During the runtime phase, the processor is caused to determine a remainder value based on the third value. The processor is caused to store the remainder value in a memory.