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Question Is the product of two consecutive integers always a multiple of 2? Why? What about the product of these consecutive integers? Is it always a multiple of 6? Why or why not? What can you say about the product of 4 consecutive integers? What about the product of five consecutive integers?
Yes, the product of two consecutive integers is always a multiple of 2. 1 × 2 = 2, 2 × 3 = 6, 5 × 6 = 30, 10 × 11 = 110, and so on. Since we know that multiplying by an odd number and an even number is always an even number. No, it is not always a multiple of 6. 1 × 2 = 2, 4 × 5 = 20, 7 × 8 = 56 Since it is not divisible by 6. The product of 4 consecutive integers 2 × 3 × 4 × 5 = 120, 4 × 5 × 6 × 7 = 840, 5 × 6 × 7 × 8 = 1680 We can say that the product of 4 consecutive integers, divisible by 12. The product of five consecutive integers is: 1 × 2 × 3 × 4 × 5 = 120, 2 × 3 × 4 × 5 × 6 = 720, 3 × 4 × 5 × 6 × 7 = 2520 Hence, we can say that the product of five consecutive integers is always divisible by 24.