Question: What is the smallest four-digit number that is divisible by 13 and ends in 7?

Sun, 03 May 2026 19:06:00 +0000

**What is the smallest four-digit number that is divisible by 13 and ends in 7?**
This quiet math puzzle has quietly gained attention among curious minds in the U.S. seeking precise, rule-based answers—especially in a digital world hungry for clear, trustworthy facts. At first glance, it sounds simple: a four-digit number, divisible by 13, ending in 7. But behind this modest challenge lies a fascinating intersection of number theory and practical number crunching. **Why This Question Is trending Now**
Mathematical riddles like this often rise in visibility during moments of digital curiosity, fueled by growing online interest in logic, patterns, and efficient problem-solving. With increased focus on numeracy and digital literacy, users seek clarity on technical questions that blend everyday relevance—like infrastructure numbers, code breakdowns, or financial thresholds—with subtle cryptographic flair. The combination of divisibility rules and final digits creates a subtle intellectual challenge without strain. **How to Find the Smallest Four-Digit Number Divisible by 13 Ending in 7**
To solve this, begin by identifying the smallest four-digit number: 1000. Test increments of 10 (to land on numbers ending in 7), checking divisibility by 13. Starting at 1007, check each number ending in 7—107, 117, 127—until reaching a multiple of 13. The first four-digit multiple of 13 ending in 7 is 1001 + 13 × k that fits the condition. Doing the math, it’s 1001 + 130 = **1001 + 130 = 1131 — ends in 1, not 7**. Continue: next is 1001 + 260 = 1261. **1261 ÷ 13 = 97, remainder 0** — and it ends in 1. Keep going: 1001 + 390 = 1391 → ends in 1 again. But 1001 + 520 = 1521 — still not.