Module · Arithmetic & Number Properties
Chapter 4: Remainders & Modular Reasoning
Arithmetic
4 topics
What this chapter covers
The 4 topics below make up Remainders & Modular Reasoning on the GRE. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Division & remainders
| Division identity | N = d·q + r, 0 ≤ r < d |
|---|---|
| Remainder range | 0 to (divisor − 1) |
| Remainder of a sum | (r₁ + r₂) mod d |
| Remainder of a product | (r₁ × r₂) mod d |
Units-digit cycles
| Cycle of 2 | 2, 4, 8, 6 (length 4) |
|---|---|
| Cycle of 3 | 3, 9, 7, 1 (length 4) |
| Cycle of 7 | 7, 9, 3, 1 (length 4) |
| Cycle of 8 | 8, 4, 2, 6 (length 4) |
| Stable digits | 0,1,5,6 repeat unchanged |
GRE reference
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