The product of four consecutive natural numbers is always divisible by:

Concept: For any k consecutive natural numbers, their product is always divisible by k factorial (k!). This holds because the product of k consecutive integers divided by k! equals a binomial coefficient — a count of combinations — which is always a whole number, so k! must divide the product exactly.

Application:

1. Here k = 4, so the guaranteed divisor is 4! = 1 × 2 × 3 × 4 = 24.

2. Take the smallest four consecutive natural numbers: 1, 2, 3, 4. Their product is 1 × 2 × 3 × 4 = 24, which is exactly divisible by 24.

3. Take a second set to confirm the pattern: 2, 3, 4, 5. Their product is 2 × 3 × 4 × 5 = 120, and 120 ÷ 24 = 5, again a whole number.

Cross-check:

• 24 ÷ 21 is not a whole number, so 21 already fails on the smallest case.

• 24 ÷ 22 is not a whole number, so 22 already fails on the smallest case.

• 24 ÷ 45 is less than one, so 45 already fails on the smallest case.

Result: the product of four consecutive natural numbers is always divisible by 24.