0
The required number is 48; its factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
When a number is expressed in its prime factorisation in power format, the number of factors of the number is the product of the power of each prime plus one, ie if n = p1^r1 × p2^r2 × ... × pm^rm, then the number of factors is given by Π(ri + 1) for i = 1, 2, ..., m.
10 can be factorised as 1 × 10 or 2 × 5.
In the first case, it would require a prime to the power 9; the smallest prime is 2 and 2^9 = 512 which exceeds 50.
Thus the only possibility is 2 × 5 which means the number is made up of 2 primes, one to the power 1 and the other to the power 4. The solution is likely to contain the two smallest primes which are 2 and 3, but which way to assign the powers. 3^4 = 81 which exceeds 50, so the choice left is 2^4 × 3^1 = 48 - the required solution.
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Jordan
Judy
Add your answer:
Earn +20 pts
What number less than 50 has the most factors?
48 has 10 factors, the most factors of any number under 50.
Which even number less than 100 has an odd number of factors and the digits of this number make up 10?
64
What number is as much more than 10 is less than one half of what 30 is 10 less than?
The number that 30 is ten less than is 40. Half that is 20. So the question becomes "what number is as much more than 10 is less than 20". This is gobbledygook, but if I rephrase to say "what number is as much more than 10 than 10 is less than 20", then since10 is less than 20 by 10, I guess 20.
10 less than a number?
N-10
What number less than 144 has the most factors?
Oh, dude, that's an easy one. The number with the most factors less than 144 is 120. It has a total of 16 factors, beating out all the other numbers below 144. So, yeah, 120 is the champ in the factor game.
