2×3×5

2×3×5 is the product of the integers 2, 3, and 5, equal to 30. The expression simultaneously represents a simple multiplication and the prime factorization of 30 into three distinct prime factors: 30 = 2 × 3 × 5. As such, 30 is squarefree and the smallest integer with exactly three distinct prime factors.

In number theory 30 is a sphenic number (the product of three distinct primes) and equals the primorial 5# (the product of all primes up to 5). Its divisor function yields eight positive divisors (1, 2, 3, 5, 6, 10, 15, 30), so the divisor-counting function τ(30) = 8. The sum of divisors σ(30) = 72 and Euler's totient φ(30) = 8. The Möbius function μ(30) = (−1)^3 = −1, reflecting its squarefree nature with an odd number of prime factors.

Because 2, 3, and 5 are the smallest primes, 30 frequently appears as a least common multiple (LCM) and convenient common denominator for fractions with denominators 2, 3, and 5. In modular arithmetic the multiplicative group of units modulo 30 has order 8, and many elementary examples in arithmetic, combinatorics, and elementary group theory use 30 as a compact, illustrative composite number.