Multiply a run of consecutive integers exactly and expose whether zero controls the result. Formula and consecutive product remain visible in one place for independent verification.
A consecutive product multiplies first, first + 1, and each following integer through the chosen count. For a run beginning at 1, the result is a factorial.
In product of consecutive integers, the relationship among the quantities matters just as much as their arithmetic.
List the integers through first + count − 1 and multiply them in small groups. Pairing factors strategically can simplify mental work without changing the product.
Six factors beginning at 5 are 5 × 6 × 7 × 8 × 9 × 10, whose product is 151,200. This Product of Consecutive Integers example can be compared with consecutive sums.
These products occur in permutations, divisibility proofs, polynomial factors, and counting formulas. Exact integer output avoids scientific-notation rounding.
Any run containing zero has product zero. Large counts create very long answers, so the page limits the number of factors to keep the browser responsive. If the Product of Consecutive Integers assumptions do not fit, consider counting arrangements.
An impossible consecutive product sign or magnitude should prompt a Product of Consecutive Integers input review before rounding.
The input labels—first integer and number of factors—encode the model used on this page. Write those labels beside source values when transferring a problem from paper or a spreadsheet. That small step catches transposed quantities and mixed units before they become a polished-looking consecutive product.
Moving a run can change every factor at once, so products grow far more rapidly than consecutive sums. A one-field trial makes this relationship visible without reworking the entire example.
Choose rounding after considering how the result will be used. Comparison may need only a few significant digits, while a later multi-step calculation benefits from carrying more. In either case, retain the page's formula with the consecutive product so the underlying definition remains visible.
A factorial begins at one; a general consecutive product may begin at any integer. The distinction determines whether this page fits the original question.
If the number moves into a spreadsheet, give its cell a consecutive product heading and retain the source values first integer and number of factors nearby. Context matters more than extra displayed digits.
When the run begins at 1.
Yes, when the run contains an odd number of negative factors and no zero.
Exact products grow rapidly in both computation and display length.