37×102

37×102 denotes the product of the integers 37 and 102. The computed value is 37 × 102 = 3774. This result can be obtained by several equivalent approaches: using the distributive property, 37 × 102 = 37 × (100 + 2) = 3700 + 74 = 3774; or by rearranging as (37 × 100) + (37 × 2) = 3700 + 74. Another common method is 102 × 37 = (100 + 2) × 37 = 3700 + 74 = 3774.

Prime factorization shows 3774 = 2 × 3 × 17 × 37. Since 102 = 2 × 3 × 17 and 37 is prime and coprime to 102, the factorization reflects the product of the two numbers. The product is even and divisible by 3, hence divisible by 6 as well; 3774 ÷ 6 = 629, which factors as 17 × 37.

In arithmetic practice, 37 × 102 serves as a straightforward example of multiplying a two-digit by a three-digit number, illustrating distributivity and the commutative property of multiplication. The result, 3774, is also the exact area of a rectangle measuring 37 units by 102 units.