A catcher's and a pitcher's uniform numbers are consecutive integers whose product is 756. If the catcher's was the smaller number, determine the uniform number of each player.
√656 = 25.6
Take it from there.
To solve this problem, let's break it down step by step:
Step 1: Find the factors of 756.
To find the factors of 756, we need to look for pairs of integers whose product is 756. Starting with 1, we find that:
1 × 756 = 756
2 × 378 = 756
3 × 252 = 756
4 × 189 = 756
6 × 126 = 756
7 × 108 = 756
9 × 84 = 756
12 × 63 = 756
14 × 54 = 756
18 × 42 = 756
21 × 36 = 756
28 × 27 = 756
These are all the pairs of numbers that multiply to give 756.
Step 2: Determine the consecutive integers.
Since the catcher's uniform number is the smaller number, we need to look for two consecutive factors from the list above. Let's examine the list:
1 × 756 = 756 (not consecutive)
2 × 378 = 756 (not consecutive)
3 × 252 = 756 (not consecutive)
4 × 189 = 756 (not consecutive)
6 × 126 = 756 (not consecutive)
7 × 108 = 756 (not consecutive)
9 × 84 = 756 (not consecutive)
12 × 63 = 756 (not consecutive)
14 × 54 = 756 (not consecutive)
18 × 42 = 756 (not consecutive)
21 × 36 = 756 (not consecutive)
28 × 27 = 756 (consecutive)
We found a pair of consecutive factors: 28 and 27.
Step 3: Determine the uniform numbers.
If 28 is the pitcher's uniform number and 27 is the catcher's uniform number, then the catcher's uniform number is the smaller one as given in the problem. Hence, the catcher's uniform number is 27, and the pitcher's uniform number is 28.
So, the uniform number of the catcher is 27, and the uniform number of the pitcher is 28.