31
31 is prime.
31
The next prime number after 29 is 31 followed by 37
32+33+34+35+36 (31 is a prime number) = 170
31
31 is prime.
31
The next prime number after 29 is 31 followed by 37
From that list, only 31 is a prime number.
It is: 29 and 31 is also a prime number
32+33+34+35+36 (31 is a prime number) = 170
It is b: 31
There are infinitely many ossible answers: 1 + 30, 2 + 29, 1 * 31, 10*3.1 2 * 15.5, 32 - 1, 33 - 2, 31/1, 62/2, etc.
31
23, 29 and 31
If you know the prime factorization of a number, you can determine the number of factors it has by looking at the possible combinations of the factors.If the prime factorization of a number is p1a * p2b *p3c , then its factors (including one and the number itself) will p1i * p2j *p3k , with i a whole number between 0 and a, j a whole number between 0 and b, and k a whole number between 0 and c.There are (a+1) numbers that i can be, (b+1) numbers that j can be, and (c+1) numbers that k can be, so there are (a+1)*(b+1)*(c+1) factors (including one and the number itself).It makes more sense using a concrete example:Consider the number 360. We want to figure out how many factors it has.It's prime factorization is 23*32*5. For a number to be a factor of 360, it will have to have only these prime factors, and the largest exponent the exponent can be for each of the factors is that factors exponent in the prime factorization of 360. So a factor of 360 will be a product of 2 (to the 0,1,2, or 3) power, 3 (to the 0,1, or 2), and 5 (to the 0 or 1 power). There are thus 4*3*2 = 24 factors of 360 (including 1 and 360). We can check this by systematically listing out the factors of 360:20*30*50=120*30*51=520*31*50=320*31*51=1520*32*50=920*32*51=4521*30*50=221*30*51=1021*31*50=621*31*51=3021*32*50=1821*32*51=9022*30*50=422*30*51=2022*31*50=1222*31*51=6022*32*50=3622*32*51=18023*30*50=823*30*51=4023*31*50=2423*31*51=12023*32*50=7223*32*51=360