Hi,
Got a few question need to ask.
1)Express 560 as a product of its prime factors(in index notation)
b)State the smallest integer value of x for which 560x is a square number
2)Write down the largest factor of 1155 other 1155 itself
3)Find the least integer value of n if 936n is a perfect square
4)A three-digit number is the product of 4 prime number. The sum of its prime factors is 30. Given that the three digits of the number are all prime and different,find the three-digit number
i) 560= 2^4 x 5 x 7
ii) We need 5 x 7
x = 35
2) 1155 = 3 x 5 x 7 x 11
largest factor = 5 x 7 x 11 = 385
3) 936 = 2^3 x 3^2 x 13
We need 2 x 13
n = 26
4)
Prime numbers are 2, 3 , 5, 7, 11, 13, 17, 19 and so on...
Since the 3 digits must all be prime, they can only be 2, 3, 5, 7. Since we only have 4 possible digits without repetition, there are only 24 combos (4P3= 24).
1. 235= 5x 47(NA) 2 primes
2. 237=3x79(NA) 2 primes
3. 253=11x23(NA) 2 primes
4. 257(NA) 1 prime
5. 273=3x7x13(NA) 3 primes
6. 275=5^2x11(NA) 3 primes
7. 325=5^2x13(NA) 3 primes
8. 327=3x109(NA) 2 primes
9. 352=2^5x11(NA) 3 primes
10. 357=3x7x17(NA) 3 primes
11. 372=2^2x3x31(NA) sum not 30
12. 375= 3x 5^3(NA) sum not 30
13. 523(NA) 1 prime
14. 527=17x31(NA) 2 primes
15. 532=2^2x7x19(NA) This is the one
16. 537=3x179(NA) 2 primes
17. 572=2^2x11x13(NA) sum not 30
18. 573=3x191(NA) 2 primes
19. 723=3x241(NA) 2 primes
20. 725=5^2x29(NA) 3 primes
21. 732=2^2x3x61(NA) sum not 30
22. 735=3x5x7^2(NA) sum not 30
23. 752=2^4x47(NA) 5 primes
24. 753=3x251(NA) 2 primes
Q4, the prime factors should be able to repeat, I believe..., i.e. 5+5+7+13
Not much time to take a look now.....
3 x 3 x 5 x19
but then de 3digit number will be 855, which doesn't fulfil...
actually gt flaw in assumption!!!
because sum of prime can also be 2 even, 2 odd
i.e. 2 + 2 + 13 + 13, 2 + 2 + 7 + 19...
2 x 2 x 7 x 19 gives you 532
Try this
2 * 2 * 7 * 19 = 532
Have to admit I got it by trial and error, on my 6th try... It's a brute force method... Don't recommend it...
I shall go sleep first... need to wake at 6.50 tmr to work...
Originally posted by eagle:Try this
2 * 2 * 7 * 19 = 532
Have to admit I got it by trial and error, on my 6th try... It's a brute force method... Don't recommend it...
I shall go sleep first... need to wake at 6.50 tmr to work...
ya I would be interested in a better method too. u go think k? :)
I only think of this...
We could have only 2 odd and 2 even prime factors, or all 4 odd prime factors, to make up the value of 30
For the first case, we have only
2 + 2 + 3 + 23 or
2 + 2 + 7 + 19 or
2 + 2 + 13 + 13
Is there anyway to prove odd prime factors being unable to give us the number we want?