An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. For example, the prime divisors of 10 are 2 and 5, and the first six primes are 2, 3, 5, 7, 11, and 13.
What are the numbers that have 6 factors?
A prime factor of a number is just a factor of that number that is also prime. So, 12 has six factors — 1, 2, 3, 4, 6, and 12 — but only two of them (2 and 3) are prime, so it has only two prime factors.
What are the 6 prime numbers?
The primes, in order, are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53.
How can you tell a prime number?
A prime number is a number greater than 1 with only two factors – themselves and 1. A prime number cannot be divided by any other numbers without leaving a remainder. An example of a prime number is 13. It can only be divided by 1 and 13.
What is the smallest number that has three diferent prime factors?
The feedback you provide will help us show you more relevant content in the future. The smallest three prime numbers are 2, 3, 5. The smallest number that has three prime factors is the product of three smalles prime factors = 2*3*5=30.
Which is the smallest integer with exactly 16 factors?
We require that this product is 16 = 2 4. Thus, the only possible values for a k are 2 4 − 1 = 15, 2 3 − 1 = 7, 2 2 − 1 = 3, 2 − 1 = 1, 1 − 1 = 0. The partitions of 4 are The smallest number with 16 divisors is thus 120. Now we count up primes, and if there is a product of primes less than a prime we counted to, we inject it in before.
Which is the smallest prime to the sixth power?
Try to prove why!) Finally, as raising a number to the sixth power is a strictly increasing function, we conclude that the smallest sixth power of a prime must be the smallest prime to the sixth power. The solution is then 2 6 = 64. I hope you get something out of seeing this proof written carefully.
Which is the smallest number f ( x ) = 4?
Write down the smallest x x for which f(x)= 4 f ( x) = 4. The smallest x x for which f(x)= 4 f ( x) = 4 will be the product of the four smallest prime numbers. So x= 2×3×5×7= 210 x = 2 × 3 × 5 × 7 = 210. Question reproduced by kind permission of Cambridge Assessment Group Archives.
