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How many primes less than 1000 are divisible by 7?
Just 7. Any other number divisible by 7 isn't prime.
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.
The largest integer that is not the product of two or more different primes?
The largest integer that is not the product of two or more different primes would be the largest prime number. Because there are an infinite number of prime numbers, there is no largest integer that is not the product of two or more different primes.
Are there more primes or composites?
In any large range of numbers, more so the higher and larger the range is, there will be more composites than primes. It is far more likely that a given number will be divisible by some number less than the number itself, the higher you go.
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.
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 least positive number divisible by two primes?
6 because it is divisible by 2 and 3.
Is 210 the lowest number divisible by 4 different primes?
Yes.
What number has exactly 3 prime different factors one which is 5 and is divisible by 11 the first digit is a square number the last two digits are different primes numbers?
935
How many positive integers less than 2101 are divisible by atleast one of the primes?
Except for 1, all of them.
Is 52563744 divisible by 24?
Sol: 24 = 3 x 8, where 3 and 8 are co-primes. The sum of the digits in the given number is 36, which is divisible by 3. So, the given number is divisible by 3. The number formed by the last 3 digits of the given number is 744, which is divisible by 8. So, the given number is divisible by 8. Thus, the given number is divisible by both 3 and 8, where 3 and 8 are co-primes. So, it is divisible by 3 x 8, i.e., 24.
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.
What is the least number that has three different prime factors?
If by "least number" you mean "smallest positive integer", then the answer is the product of the three smallest primes: 2x3x5 = 30
Is 1250 a prime number?
No, it is not a prime number, it is divisible by 2, 625, 5, 250, 10, 125, and probabaly more than that. Primes are only divisible by 1 and itself.
How many primes less than 1000 are divisible by 7?
Just 7. Any other number divisible by 7 isn't prime.
Is there a number less than 200 that is divisible by four different prime numbers?
No. The 4 smallest primes are 2 3 5 7. Multiplying these gives 210. Note that 1 is not regarded as a prime no. If it were to be then no other number could be prime for all of them are divisible by 1.
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.
