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64: 1, 2, 4, 8, 16, 32, 64

Tip: To find the number, consider that if there are an odd number of factors, the number must be a perfect square, because a perfect square has one factor that is multiplied by itself. 64: 1, 2, 4, 8, 16, 32, 64

Tip: To find the number, consider that if there are an odd number of factors, the number must be a perfect square, because a perfect square has one factor that is multiplied by itself.

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Q: What is the least whole number with exactly seven positive divisors?

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It is 6.

6

The least positive number is 18.

Least number with exactly n even divisors 1 -> 0 divisor 2 -> 1 divisor 4 -> 2 divisors = 22 8 -> 3 divisors = 23 12 -> 4 divisors = 22x3 32 -> 5 divisors = 24

Yes. Every number is divisible by itself or 1.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more whole numbers.

It is 4096.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more wholenumbers.

The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more given whole numbers.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more whole numbers.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more wholenumbers.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more whole numbers.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more wholenumbers.

The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more given whole numbers.

An integer (call it 'x') has exactly 3 divisors if and only if it is the square of a prime number. In other words, to generate a list of integers with exactly 3 divisors, just keep squaring prime numbers. A number with 3 divisors cannot be prime (a prime number has only 2 divisors, 1 and itself). So it must be a composite number, which is a number that can be factored as a product of prime numbers (Fundamental Theorem of Arithmetic) -- i.e. a composite number must have at least one prime divisor. In the case where the number has only 3 divisors, two of them are 1 and the number itself (neither of which are prime). Therefore the third divisor must be a prime number. So the three divisors of 'x' are: 1, p, x where p is prime. Now since p is a divisor (or factor) of x, and the only other divisor besides 1 and x itself, x must equal p*p -- or x=p^2 . Obvious x can't equal p*x and if x = p*1, x=p so x is prime, or has only 2 divisors... If x = p^(3) , then x = p*p* p , or p*(p^2) ... this means that p^2 would also have to be a divisor of x, and this would contradict with x having only 3 divisors. For the same reason, x = p^(greater than 3) is also not possible. So the only possibility is that an integer with exactly 3 divisors is the square of a prime number "p". The divisors are 1, p, and p^2. I'm sure there's a simpler, more elegant way of explaining this, but it should be clear enough.

The number 1.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more given whole numbers.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more given whole numbers.

None. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more given whole numbers.