98
7
no, factors of a number would be less than that of the original number. A prime number is a number that has factors of only itself and 1.
For a number to be a perfect square, its prime factors must be separable into two identical sets. For a number to be a perfect cube, its prime factors must be separable into three identical sets. For a number to be a perfect 'fifth', its prime factors must be separable into five identical sets. ---- If N x 2 is separable into two identical sets of prime factors, then: * N must have an odd number of 2's in its prime factorisation. * All other prime factors of N must occur an even number of times. If N x 3 is separable into three identical sets of prime factors, then: * The prime factorisation of N must contain a number of 3's that is one less than a multiple of three. * All other prime factors of N must occur a number of times that is already a multiple of three. If N x 5 is separable into five identical sets of prime factors, then: * The prime factorisation of N must contain a number of 5's that is one less than a multiple of five. * All other prime factors of N must occur a number of times that is already a multiple of five. ---- From the above, we know that N's prime factorisation must contain 2's, 3's and 5's. How many times does 2 appear in the prime factorisation of N? - It must be an odd number. - It must be a multiple of three. - It must be a multiple of five. The smallest valid frequency is 15. How many times does 3 appear in the prime factorisation of N? - It must be an even number. - It must be one less than a multiple of three. - It must be a multiple of five. The smallest valid frequency is 20. How many times does 5 appear in the prime factorisation of N? - It must be an even number. - It must be a multiple of three. - It must be one less than a multiple of five. The smallest valid frequency is 24. ---- Therefore N = 215 x 320 x 524 = 6810125783203125000000000000000. That seems to be the smallest possible value.
No.3 is less than 5, thus cannot be a multiple of it; 3 is prime, therefore cannot be a multiple of any number besides 3 (which is one of its factors); by definition, 3 is ismply not a multiple of any number but 1 and 3.
How about 105 whose prime factors are 3, 5 and 7
It is 30.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
It is 97 which has only two factors because it is a prime number
210
A number is prime if its only two factors are one and itself.
512 = 29 or 768 = 28*3 have 9 prime factors each.
Numbers can be checked to see if they are primes simply by factoring them. Every prime number has exactly two factors, 1 and the number itself. If there are more or less than 2 factors, the number is not a prime. 1 has only one factor so it is not a prime, and composite numbers have 3 or more factors.