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Q: Three digit number greater than 500 has five consecutive numbers among its factors?

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The greater number of the three is 26.

Any multiple of 60 from 540 to 960

3 consecutive numbers cannot be prime factors. Any three consecutive numbers would include at least one even number. The only even prime number is 2, and (2,3,4) doesn't qualify.

There are two consecutive odd numbers such that five times the smaller plus twice the greater is 25. What is the smaller number?

695

2 and 3 are consecutive prime numbers; therefore, such a concept does exist, but those are the only two consecutive primes. The reason there are not any others: natural numbers alternate between odd and even numbers. When the number is even, then 2 is a factor. The number 2 is the only even prime number (it's only factors are 2 and 1). All other even numbers have factors, in addition to 2 & 1. So if a number is prime, and the number is not 2, then it is an odd number. The two numbers on either side of an odd number are even. So if the prime number is greater than 3, then the two numbers on either side of it will be even numbers, which are not primes.

Every number greater than 1 has the two factors 1 and the number itself.

The sum of 2 consecutive numbers cannot be 118, because you cannot get an even number when you add an even and an odd number.

Numbers that have only two factors are prime numbers. You're looking for the next three prime numbers over a certain number. But, you didn't tell us what number the three numbers have to be greater than.

Any three-digit multiple of 60, from 120 to 960, has the first five counting numbers as factors.

13, or any number greater than 5280.

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