There are three different integers and the product of the three integers is larger than the sum of the three integers by four.
There are two sets of group of such three integers.
Largest integer is 4 in one group.
Find the each product of two groups.
There are two sets of group of such three integers.
Largest integer is 4 in one group.
Find the each product of two groups.
Answer
Since the product of 4 × B × C is an even number, the sum of 4 + B + C + 4 is also even number and the sum of B + C is also an even number.
Combination of B + C is an odd + odd.
Then searching for a combination of B and C, it is 1 and 3.
Therefore, the product of the three integers is 4 × 3 × 1 = 12.
Next, start considering the product 13 following 12.
There is a combination of the product of 13 = 1 × 1 × 13, but it is not suitable to the condition.
There are two combinations of the products of 14 = 1 × 1 × 14 and 1 × 2 × 7.
1 × 1 × 14 is not applied.
1 × 2 × 7 = 1 +2 +7 +4 = 14.
Then the product of the three integers is 14.
12 and 14
Solution
Three integers are set to A, B, and C and assuming A = 4, then 4 × B × C = 4 + B + C + 4.
Since the product of 4 × B × C is an even number, the sum of 4 + B + C + 4 is also even number and the sum of B + C is also an even number.
Combination of B + C is an odd + odd.
Then searching for a combination of B and C, it is 1 and 3.
Therefore, the product of the three integers is 4 × 3 × 1 = 12.
Next, start considering the product 13 following 12.
There is a combination of the product of 13 = 1 × 1 × 13, but it is not suitable to the condition.
There are two combinations of the products of 14 = 1 × 1 × 14 and 1 × 2 × 7.
1 × 1 × 14 is not applied.
1 × 2 × 7 = 1 +2 +7 +4 = 14.
Then the product of the three integers is 14.
