0
The largest 2-digit number with only 4 factors is 77. The factors of 77 are 1, 7, 11, and 77. In general, numbers with exactly 4 factors are of the form p^3, where p is a Prime number. In this case, 77 can be expressed as 7^3.
99 with {3, 9, 11, 33}
or
81 with {1, 3, 9, 27} or {3, 9, 27, 81} respectively
or
95 with {1, 5, 19, 95}.
Long answer:In general, if a number n has the prime factorization
n = p1k1 · p2k2· p3k3 · ... · pmkm
then the number of divisors including 1 and n itself is
#{z : z|n} = (k1+1) · (k2+1) · ... · (km+1)
because you can pick each prime factor not at all (0 times), 1 time, 2 times, ... or k times in order to compose a distinct divisor of n.
Thus, if you e.g. only ask for non-trivial divisors you need to find ki such that
(k1+1) · (k2+1) · ... · (km+1) -2 = 4.
In other words
(k1+1) · (k2+1) · ... · (km+1) = 6 = 2 · 3 · 1 · 1 · ... · 1,
which is only possible if one bracket yields 2, another 3 and all the remaining ones 1.
So k1=1, k2=2 and k3=k4=...km=0, thus n must consist of precisely two unique primes:
n = p11 · p22.
Indeed, then the non-trivial factors are: p1, p2, p1·p2 and p22.
Luckily, the highest two-digit number (being 99) already fulfills this condition (p1=11, p2=3). :-)
Good day
Add your answer:
Earn +20 pts
The largest two digit number with only 3 factors?
49
What is the largest two digit number with only 3 factors?
49
What is the largest three-digit number that has only 2 and 5 as prime factors?
800 2x2x2x2x2x5x5
What is the smallest 2 digit number that has only four factors?
10
What is the smallest 2 digit number with only 2 factors?
It is 11 which is a prime number whose factors are itself and one
What is the largest 2 digit number with only 3 factors?
49
The largest two digit number with only 3 factors?
49
What is the largest 2 digit number with only 2 factors?
97
What is the largest 2 digit number with only 10 factors?
48
What is the largest two digit number with only 3 factors?
49
What is the largest 2 digit number with only 6 factors?
It is 99.
What is the largest 3-digit number that only has 2 and 5 as prime factors?
The only number that ONLY has two and five as factors is 10, which has two digits, so there are no numbers that are three digits long and ONLY have two and five for factors. However, if you are asking what the largest three digit number that has two and five for factors, it would be the largest three digit number with ten as a factor, as ten the the LCM of two and five, and that would be 390.
What is the largest two digit number with 3 and 7 as its only prime factors?
63 is.
What is the largest three digit number that has four factors?
If factors include 1 and the number itself then the any number (n) with only 4 factors has to be the product of two prime numbers, p1 and p2. The factors are then n, p1, p2, and 1. The largest 3-digit number with only 4 factors is 998. The factors are 998, 499, 2 and 1
What is the largest three-digit number that has only 2 and 5 as prime factors?
800 2x2x2x2x2x5x5
What is the largest 2 digit prime number?
97A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite. 97 is the largest 2 digit prime number.
What is the largest three digit number with a digit sum of nine?
900 It is the only three digit number with a nine in the numbers place
