Question: What is the smallest three-digit number that is a multiple of 9 and leaves a remainder of 2 when divided by 5? - Sterling Industries
What is the smallest three-digit number that is a multiple of 9 and leaves a remainder of 2 when divided by 5?
This precise question blends two well-known number rules—a cornerstone of early math and a common puzzle in modular arithmetic—sparking curiosity among US learners, educators, and problem-solvers. As curiosity around logic puzzles and number patterns grows, particularly online, this type of query reflects a deeper interest in pattern recognition and practical math.
What is the smallest three-digit number that is a multiple of 9 and leaves a remainder of 2 when divided by 5?
This precise question blends two well-known number rules—a cornerstone of early math and a common puzzle in modular arithmetic—sparking curiosity among US learners, educators, and problem-solvers. As curiosity around logic puzzles and number patterns grows, particularly online, this type of query reflects a deeper interest in pattern recognition and practical math.
What is the smallest three-digit number that is a multiple of 9 and leaves a remainder of 2 when divided by 5?
At first glance, combining divisibility by 9 with a remainder of 2 modulo 5 seems simple—but lies a subtle compatibility problem. Multiples of 9 follow a clean sequence: 108, 117, 126, 135, ... But the remainder condition—numbers that are 2 more than multiples of 5—forces a shift to modular reasoning. To find the answer, one must search through three-digit multiples of 9 and test which satisfy the second condition.
Understanding the Context
Why This Question Is Resonating in 2025
Today’s digital landscape rewards quick mental math and pattern-based puzzles, especially in mobile-first contexts where curiosity fuels scrolling. The intersection of arithmetic rules sparks gentle cognitive engagement, ideal for SEO and Discover visibility. With rising interest in STEM basics and interactive learning apps, such puzzles farm curiosity into deep dives. Users aren’t just seeking numbers—they’re testing systems, sharpening logic, and satisfying instant gratification through discovery.
How It Works: A Step-by-Step Breakdown
To solve, begin with the smallest three-digit multiple of 9: 108.
Then test each successive multiple—117, 126, 135—until finding one that leaves remainder 2 when divided by 5.
Numbers leaving remainder 2 when divided by 5 end in: 2, 7, 12, 17, 22, 27, ..., or equivalently, numbers congruent to 2 mod 5 (n ≡ 2 mod 5).
Because multiples of 9 are divisible by 9, they’re also congruent to 0 mod 3 and mod 9.
Key Insights
Instead of lengthy math, compute each multiple of 9 from 108 upward, checking:
- Does (n – 2) divide evenly by 5?
That is, is
