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Find the prime factorization of each number:
Take the lowest power of each common prime factor:
Question: How many positive 3-digit numbers are divisible by 15?
The smallest 3-digit number divisible by 15 is 105, and the largest is 990.
Use the formula for the $n$-th term of an arithmetic sequence:
Question: A scientist is designing a governance model for a futuristic city and proposes that the number of decision nodes and feedback loops should be in the ratio $4:11$. If there are 44 feedback loops, how many decision nodes are needed?
The ratio of decision nodes to feedback loops is $4:11$. Since there are 44 feedback loops, we find the value of one part:
Now, multiply one part by the number of decision node parts:
Question: Expand and simplify the expression $(3x - 2y)(x + 5y)$.
Question: What is the greatest common factor of 72 and 90?