2006-08-15 04:44:06 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Notice that 4891=4900-9=70^2 -3^2=(70-3)(70+3)=67*73, so it isn't prime.
2006-08-15 06:37:23 · answer #1 · answered by mathematician 7 · 1⤊ 0⤋
Find the greatest integer less than sqrt(4891). It is 69.
Check for divisors of 4891 <= 69.
It is enough if you check for odd prime numbers.
Here again you can leave 5 as the number does not end with 5.
To check for 3 and 11 you can use the divisiblity rules.
Clearly it is not divisible by 3, 7, l1.
The rest are 13, 17, 19, 23, 29, 31,37, 41, 43, 47, 53, 59, 61, 67.
Also you can judiciously combine the primes which when multiplied give 1 in the units place.
This way you can minimise your work.
2006-08-15 12:35:38 · answer #2 · answered by baskaran r 2 · 0⤊ 0⤋
4891 isn't that large of a number. If it has any prime factors (other than itself an 1), they'll be less than its square root, which is about 69.9. So you just need to try all the primes from 2 to 69.
Actually, we can eliminate 2 (because the number's not even), and 3 (because the digits don't add up to to a multiple of 3), and 5 (because the number doesn't end in 5 or 0), and 69 isn't even prime, so you really just need to test the primes from 7 to 67.
Good luck!
2006-08-15 11:50:26 · answer #3 · answered by Jay H 5 · 1⤊ 0⤋
To find out whether a number is prime, you must try to divide it by ALL PRIME NUMBERS UP TO (AND INCLUDING) THE SQUARE ROOT of number itself. In your case, all prime numbers up to 69:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67
It is not divisible through any of these, so the number is prime.
2006-08-15 11:54:31 · answer #4 · answered by dutch_prof 4 · 0⤊ 0⤋
Look at the last number in the entire number, which is 1. Take PRIME numbers the multiply into other numbers that end with one...such as 11, 21 or 51.
11x1=11
21x1=21
7x3=21
17x3=51
51x1=51
so take the numbers 11, 21, 7, 3, 17, and 51 and divide that number by those and this should give you a good idea whether or not it is prime.
2006-08-15 12:10:11 · answer #5 · answered by Dunc 1 · 0⤊ 0⤋
By "on one's own" does that mean by hand without help? Then I agree to all those people who tells you to see if 4891 is divisible by all the primes that are less than its square root. I also might suggest a programmable calculator that has such a program in it (whether you programed it yourself or it comes with it). It might be easier than going on the internet all the time.
2006-08-15 12:39:17 · answer #6 · answered by Linda O'Chuffy 2 · 1⤊ 0⤋
square root of 4891 is 69.9... so try to divide 4891 by all odd numbers from 3 to 69 and see if prime
2006-08-18 02:29:21 · answer #7 · answered by Anonymous · 0⤊ 0⤋
find the sq rt of 4891=lies between 69 and 70
so try for divisibility by prime nos upto 69
2006-08-15 11:52:19 · answer #8 · answered by raj 7 · 0⤊ 0⤋
square root of 4891 is 69.9... so try to divide 4891 by all odd numbers from 3 to 69 and see if prime.
2006-08-15 11:50:16 · answer #9 · answered by starr_man 1 · 2⤊ 1⤋
The Sieve of Eratosthenes. Divide by all primes under the square root (up to 67). If none of them divide it exactly, it is prime,
2006-08-15 11:50:39 · answer #10 · answered by brucebirchall 7 · 1⤊ 0⤋