Open Middle®
Directions: What is the smallest number, greater than zero, that is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10?
Hint
Does the number have to be even or odd? How do you know?
What digit must be in the ones place? How do you know?
The sum of the digits must be equal to a multiple of what number?
What digit must be in the ones place? How do you know?
The sum of the digits must be equal to a multiple of what number?
Answer
2,520
Source: Brian Lack
Rather than being divisible by various numbers, what if there is a remainder?
For example:
Suppose you divide a number by 2 and the remainder is 1.
Suppose, further, that when you divide this number by 3, 4, 5, 6, and 7, the remainder in each case is 1.
What is the smallest positive number that satisfies the constraints above?
Rather than being divisible by various numbers,what if there is a remainder?
For example:
Suppose you divide a number by 2 and the remainder is q.
Suppose,further,that when you divide this number by 3, 4, 5,6, and 7, the remainder in each case is 1.
What is the smallest positive number that satisfies the constraints above?
as the problem is stated, i don’t think there is an answer.
.001 is divisible by all the numbers 1, through 10, as is .0001, and .00001.
it is not *wholly* divisible by any of the numbers; however, this is not a condition in the problem setup.
What about asking, “What is the smallest natural number that yields remainder 1 under division by any set of consecutive natural numbers beginning with 1”?
Now that’s a problem, and was a big hit with my sophomores. Generalization to the extreme.
And then what if we open this up to division by just any set of consecutive natural numbers — not necessarily beginning with 1?
Number can negative right ? So it will change
2520
2,520 is the answer for the question
2,520
Could the answer be 1?
It is a prime number