24 is the lowest 2 digit number with 8 factors. Let the number be N. If p, q, r, s, … are the prime factors of N, and N = (p^a)*(q^b)*(r^c)*…, the number of factors including 1 and N is (a + 1)*(b + 1)*(c + 1)*… As 21 = 3*7 and 35 = 5*7, it is clear that 3, 5 and 7 are factors of N.
How do you find the factors of big numbers?
To calculate the factors of large numbers, divide the numbers with the least prime number, i.e. 2. If the number is not divisible by 2, move to the next prime numbers, i.e. 3 and so on until 1 is reached. Below is an example to find the factors of a large number.
What is the largest 2 digit number with 9 factors?
There aren’t too many 2 digit square numbers, so lets just take it from the top. Working backwards, the largest 2 digit number with exactly 9 factors is 36. its very easy as you have asked for an odd number of factors then the number should be a perfect square
Which is the smallest integer that has exactly 7 factors?
In that case it means the interesting numbers for factors are the numbers that themselves have large numbers of small prime factors. For example, we could choose 2 4 = 16 factors. The simple algorithm would suggest the answer is 2 ⋅ 3 ⋅ 5 ⋅ 7 = 210 but 2 3 ⋅ 3 ⋅ 5 = 120 is smaller. Hence 2 6 ⋅ 3 = 192 factors might be an interesting question…
Is there a number that has exactly 7 factors?
The Rule of product then proves the claim. These two facts, together with the fact that 7 is prime, tell us that any number with exactly 7 factors must be equal to the sixth power of a prime number. (Do you see why? Try to prove why!)
How to calculate all factors of a number?
Example: All the factors of 20. Start at 1: 1×20=20, so put 1 at the start, and put its “partner” 20 at the other end: Then go to 2. 2×10=20, so put in 2 and 10: Then go to 3. 3 doesn’t work (3×6=18, 3×7=21). There is no whole number between 4 and 5 so you are done! (Don’t forget the negative ones). Is That How The Calculator Works?
