14×101

14×101 is the product of the integers 14 and 101. The result is 1414. This can be shown by the distributive property: 14×101 = 14×(100+1) = 1400 + 14 = 1414.

The prime factorization of the product is 1414 = 2 × 7 × 101, since 14 = 2×7 and 101 is a prime number. Because 101 shares no prime factors with 14, gcd(14,101) = 1, and the product has three distinct prime factors, making 1414 square-free.

In arithmetic practice, 14×101 is often used as an example of multiplying by a two-digit number ending in 1, illustrating the distributive property and mental math strategies. The identity 14×101 = 14×100 + 14 = 1414 demonstrates how multiplication by 101 can be decomposed into a subtraction-free calculation involving 100 and the original number.

Contextually, 101 is a prime commonly encountered in teaching primality and factorization, while 14 is a small composite number with factors 2 and 7. The product 1414 is even and four-digit, with prime factors 2, 7, and 101.