How Many Numbers Between 400 and 800 Are Divisible by Both 88 and 72?

Only one number between 400 and 800 is divisible by both 88 and 72.

Finding the Solution

To find the numbers divisible by both 88 and 72, we need to find the least common multiple (LCM) of 88 and 72.

1. Prime Factorization: First, find the prime factorization of each number:

   • 88 = 2³ x 11
   • 72 = 2³ x 3²

2. Least Common Multiple (LCM): The LCM is found by taking the highest power of each prime factor present in the factorizations:

   • LCM(88, 72) = 2³ x 3² x 11 = 8 x 9 x 11 = 792

3. Checking the Range: The LCM, 792, falls within the range of 400 to 800. Any other number divisible by both 88 and 72 would be a multiple of 792. The next multiple of 792 (792 x 2 = 1584) is greater than 800.

Therefore, only 792 is divisible by both 88 and 72 within the specified range.

References Supporting the Answer

Multiple sources confirm this finding:

• Quora: A Quora answer explicitly states that 792 is the only number between 400 and 800 divisible by both 88 and 72. https://www.quora.com/How-many-numbers-between-400-and-800-are-divisible-by-both-88-and-72

• Brainly: A Brainly answer arrives at the same conclusion by calculating the LCM and observing its position within the range. https://brainly.in/question/15447156