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Q: How many positive integers less than 2101 are divisible by atleast one of the primes?
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Related questions

What is the least positive number that is divisible by three different primes?

30, which is the smallest positive integer divisible by the first three primes: 2, 3 and 5.


What is the least positive number divisible by two primes?

6 because it is divisible by 2 and 3.


What are the categories of integers?

Positive and negative, would be one category of them, but primes and non-primes would be another, and evens or odds, another.


Find smallest positive divisor of an integers other then 1?

There is no such number. If you restrict yourself to integers, there are numbers - such as primes, that are not divisible by an integer other than one. And if you do not restrict yourself to intgers, then there is no smallest number sincce given any number, half that number will be smaller and will be a divisor.


How many of the first 10 positive integers are primes?

There are 4 and they are 2 3 5 and 7


What is the greatest 8 digit even prime number?

There is none. The only even prime number (even meaning divisible by two, and primes being numbers divisible only by the integers 1 and themselves) is 2.


What do the numbers 46 and 15 have in common?

They are composite positive integers. They are semi-primes.


Is 43.2 a prime number?

Only integers (whole numbers) can be primes. A prime is a number that is only divisible by 1 and itself. 43.2 and all other decimal numbers are not divisible by 1.


Is there a number from 1 to 100 that is divisible by four different primes?

no the smallest number that is divisible by four different primes would be 210


What is the name of the product that has more than one factor?

A composite number. Actually, all integers have at least two factors. Even primes are divisible by 1 and themselves.


If some numbers are integers and others prime- are all prime?

All primes are integers, but all integers are not prime.


What is the smallest prime number including negatives?

Negative numbers are not considered primes. Prime numbers are defined for positive integers. The smalles prime number is 2. by Alexis Assad


If some integers are prime then are all numbers primes?

No.


Is 51 and 53 twin primes?

No - 51 is divisible by 3.


What is the square of the sum of two primes?

There is no particular characteristic that is common to such numbers other than they are positive integers greater than or equal to 4.


Is 210 the lowest number divisible by 4 different primes?

Yes.


Proof that there are no three consecutive primes except 3 5 and 7?

Let p, p+2, and p+4 be three consecutive odd numbers. Then, if p ≡ 0 (mod 3), p is divisible by 3; if p ≡ 1 (mod 3), then p+2 is divisible by 3, and if p ≡ 2 (mod 3), then p+4 is divisible by 3. That is, at least one of p, p+2, and p+4 must be divisible by 3. The only prime that can be divisible by 3 is 3 itself; for any other positive integer divisible by 3 must have another factor, making it composite. This gives the possibilities -1, 1, 3 1, 3, 5 3, 5, 7 The first two are eliminated because -1 and 1 are not primes, leaving 3, 5, 7 as the only set of three consecutive integers that are all prime.


Can you find a number less than 200 that is divisible by 4 primes?

No. The smallest 4 primes are 2, 3, 5 and 7 and their product is 210.


Is 224 a product of prime numbers?

Yes. In fact, all positive integers (except primes) can be represented as the product of prime numbers. In this case, 224 = 2 * 2 * 2 * 2 * 2 * 7


What does Phi mean in mathematics?

the phi of n is the number of positive integers below n which do not share any factors with it. for example, the phi of 30 is 8 because it does not share any factors with 8 numbers: 1,7,11,13,17,19,23,29 these are called co-primes


Which are the numbers which are neither prime nor composite and why?

All primes have two positive divisors. There are only two integers that are neither composite or prime and they are 1 and 0. The number 1 has only 1 positive divisor, itself. The number 0 has an infinite number of divisors.


Is 12.5 a prime number?

No. Only integers can be primes (two close by are 11 and 13)


The smallest nonzero number that is a multiple of two or more numbers?

If you meant different primes then 2*3 = 6 If you did meant primes, but not necessarily different, then 2*2 = 4 If you meant different integers then 1*2 = 2 If you meant integers, but not necessarily different, then 1*1 = 1 And if you did not mean integers, then there is no such number. Your search will take you to infinitesimally small fractions - closer and closer to 0 but never actually reaching it. All of the above assume that the numbers being multiplied together are positive. If not, the answer will tend to minus infinity.


How many primes less than 1000 are divisible by 7?

Just 7. Any other number divisible by 7 isn't prime.


If told that 'q' 'p' and 'r' are distinct primes and that there exists 'n' such that 'n equals p x q x r' How many positive factors of 'n' are there and How do you determine what they are?

If p, q and r are distinct primes and n=pxqxr then n will have 8 factors, all of which will be positive since prime numbers are all positive, which are: n(pqr), pq, pr, qr, p, q, r and 1. Here there were 3 distinct primes so the number of positive factors is 2^3. In general if you had p distinct primes then you would have 2^p positive factors.