Question: How many positive integers less than 50 are multiples of 5 or 7 but not both?

Sun, 03 May 2026 11:37:06 +0000

**How Many Positive Integers Less Than 50 Are Multiples of 5 or 7 but Not Both?**
*Discover why this straightforward math question is catching attention in the U.S. – complex enough to spark curiosity, simple enough to inform curiosity-driven searches.* Ever wondered how many numbers under 50 fit the pattern of being multiples of 5 *or* 7, but not both? This seemingly simple question is more than just a math riddle – it reflects growing interest in logic, patterns, and practical number sense in a fast-paced digital world. With mobile users seeking quick, meaningful insights, understanding how to isolate “exclusive” groups within a set has become both a mental exercise and a valuable skill. **Why This Question Is Rising in Search
in the U.S.**
Across the United States, users are increasingly curious about patterns in data, especially in finance, budgeting, personal development, and even gaming or scanning trends. The question “How many positive integers less than 50 are multiples of 5 or 7 but not both?” taps into that mindset—encouraging precise thinking without complexity. It leverages familiar numbers (multiples of core integers like 5 and 7) and the constraint of “not both,” making it ideal for search intent rooted in categorization and exclusion. As users seek clarity amid digital noise, questions like this deliver credible, digestible answers—ideal for mobile-first discovery. **What the Question Actually Counts**
To answer clearly: among the positive integers from 1 to 49, the multiples of 5 (5, 10, 15, 20, 25, 30, 35, 40, 45) total 9 numbers. The multiples of 7 (7, 14, 21, 28, 35, 42, 49) total 7 numbers. The overlap—multiples of both 5 and 7—is those divisible by 35: only 35 (1 number).
Using the principle of set logic:
Total multiples of 5 or 7 = 9 + 7 – 1 = 15
But since “but not both” excludes the overlap, subtract the 1 shared multiple:
15 – 1 = **14** numbers meet the criteria.
This method confirms the count with precision, appealing to analytical minds.