5 × 23 × 2 = 230
414 = 2 X 207 = 2 X 9 X 23 = 2 X 3 X 3 X 23. So the prime factorization of 414 is 2 X 32 X 23.
1 x 46, 2 x 23, 23 x 2, 46 x 1
1 x 46, 2 x 23, 23 x 2, 46 x 1 = 46
2 x 2 x 2 x 3 x 23
Prime factors: 2, 3, 23, 23 Others are combinations of the above, i.e. 2 x 3 = 6 2 x 23 = 46 3 x 23 = 69 2 x 3 x 23 = 138 23 x 23 = 529 2 x 23 x 23 = 1058 3 x 23 x 23 = 1587
PF of 2,116 = 2 x 2 x 23 x 23 or 22 x 232
The prime factorization of 92 is: 2 x 2 x 23 or 2^2*232 x 2 x 232 x 2 x 23 = 922 x 2 x 23 = 92
Prime factors are 2, 2, 2, 7, 23 Others are combinations of the prime factors, i.e. 2 x 2 = 4 2 x 2 x 2 = 8 2 x 7 = 14 2 x 2 x 7 = 28 2 x 23 = 46 2 x 2 x 2 x 7 = 56 2 x 2 x 23 = 96 7 x 23 = 171 2 x 2 x 2 x 23 = 184 2 x 7 x 23 = 322 2 x 2 x 7 x 23 = 644
(23/2)2 x2 - 23x = 0 x2 - 23x + (23/2)2 = (23/2)2 (x - 23/2)2 = (23/2)2 x - 23/2 = 23/2 x = 23/2 + 23/2 x = 23 Of course you could come to this solution much more easily by dividing the whole equation by x at the start. There really is no need to complete the square in this case: x2 - 23x = 0 x - 23 = 0 x = 23
Prime factors are 2, 2, 3 3, 23 Other factors are combinations of primes, i.e. 2 x 2 = 4 2 x 3 = 6 3 x 3 = 9 2 x 2 x 3 = 12 2 x 3 x 3 = 18 2 x 2 x 3 x 3 = 36 2 x 23 = 46 3 x 23 = 69 2 x 2 x 23 = 92 2 x 3 x 23 = 138 3 x 3 x 23 = 207 2 x 2 x 3 x 23 = 276 2 x 3 x 3 x 23 = 414
2 x 2 x 3 x 3 x 23 22 x 32 x 23
4968 = 2 x 2 x 2 x 3 x 3 x 3 x 23 or 23 x 33 x 23
The prime factors of 92 are: 2 x 2 x 23 22 x 23
2 x 46 4 x 23 2 x 2 x 23
64 = 8 x 8 = 23 x 23 = 2 x 2 x 2 x 2 x 2 x 2 = 26
5 × 23 × 2 = 230