Ten (number)

Mathematical properties

As a natural number, ten has several elementary mathematical features: it is even and composite, with prime factorization 2 × 5. Its positive divisors are 1, 2, 5 and 10. In polygonal number theory, 10 is the fourth triangular number (1+2+3+4) and appears in simple combinatorial contexts. In positional notation it acts as the base for the decimal system, which uses ten distinct digits (0–9).

Numeral systems and notation

Ten has been written and represented in many ways across history. In the Roman system it is denoted by X. In binary, the base‑2 representation of ten is 1010. The central role of ten in everyday arithmetic comes from the base‑10 (decimal) system; see decimal notation for details about place value and multiples of ten.

Uses and cultural significance

Ten commonly appears in measurement, ranking and notation. Metric prefixes and scales often rely on powers of ten, which simplifies conversions. Rating systems use ten as a round top score (for example, "ten out of ten"). Ten is also a familiar unit in grouping: decades in time, lists that use tens, and many educational or organizational practices count by tens for convenience.

Examples and distinctions

• Arithmetic: multiplying or dividing by ten shifts digits in decimal notation (adding or removing a trailing zero).
• Representation: ten in Roman numerals is X; in binary it is 1010; in spoken language it often begins compound numbers (ten‑one = eleven).
• Cultural: the number is used symbolically to indicate completeness, a benchmark, or a full set in many traditions.

Because of its central place in counting and measurement, ten functions both as a practical tool in computation and as a frequent reference point in social, educational and scientific contexts. Its ubiquity in notation and everyday usage makes it one of the most recognizable numbers worldwide.