What number less than 1000 has the most prime factors?
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What number less than 1000 has the most prime factors?
Prime factorising 100 gives us 2\times2\times5\times5, now we can assign the smallest prime bases to the largest powers, which will give us 24$\times34\times5\times7 = 45360. Sanika and Amy both said that the number under 1000 with the most factors is 840 (32 factors).
What numbers have the most divisors?
The late mathematician Jean-Pierre Kahane has suggested that Plato, must have known about composite numbers as he deliberately chose 5040 as the ideal number of citizens in a city as 5040 has more divisors than any numbers less than it….Examples.
| n | d(n) | Divisors of n |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 1, 2 |
| 4 | 3 | 1, 2, 4 |
| 6 | 4 | 1, 2, 3, 6 |
Which positive integer in 1 1000 has the maximum number of divisors?
So 840 has the maximum number of divisors among all the numbers between 1 & 1000.
How many prime factors do 1000 have?
Factors of 1000: 1 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500,and 1000. Prime Factorization of 1000: 1000 = 2 × 2 × 2 × 5 × 5 × 5. What Are the Factors of 1000?
Does 1 have a prime factorization?
The number 1 is called a unit. It has no prime factors and is neither prime nor composite.
How many factors does 1000 have?
Hence, the factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 250, 500 and 1000. Thus, the total number of factors are 16.
Is the biggest prime number?
Currently, the largest known prime number is 282,589,933−1. This prime, along with the previous seven largest primes to be discovered, are known as Mersenne primes, named after the French mathematician Marin Mersenne (1588–1648).
How many divisors does 1000 have?
Total number of divisors of 1000 are 16 including 1 and 1000. We want divisors of 1000 including 1 but excluding 1000 so answer is 15.
How many divisors are there for 10000 including 1 & 10000?
There are two numbers between 1 and 10000 that have 64 divisors, 7560 and 9240.
What number has the most factors between 1 and 1000?
512, out of all then numbers between 1 and 1000, has the most (9 total) numbers in its prime factorization. However, since the only numbers in the prime factorization in 2, it only has 11 factors, including 1 and itself. Now, take . That product is 2310, which is above 1000.
What can go into 87?
The factors of 87 are 1, 3, 29, and 87.