There are many ways and these depend on your fluency with number and their inter-relations.
For example, since I know that 17^2 = 289 so I would do
18*34 = (17+1)*(2*17) = 2*17^2 + 2*17 = 2*289 + 2*17 = 2*(289+17) = 2*306 = 612. Of course, I would not go through all those steps but they are shown there so that you may be able to follow.
An alternative would be to multiply 18 by 4 and 30 and then to sum the answers:
18*4 = 72, 18*30 = 540 and so the answer is 72+540 = 612.
This is equivalent to 18*34 = 18*(30 + 4)
Yet another method, attributed to Euclid is to halve the smaller number and double the other, ignoring halves, and keep going until the smaller number reaches 1.
18 ... 34
9 ... 68
4 ... 136
2 ... 272
1 ... 544
Then add together the larger numbers for which the left hand number is odd. Thus 68 + 544 = 612.
You can multiply 2 and 9 to get 18. Alternatively, you can multiply 3 and 6 to get 18 as well.
2*17 = 34
17 x 2 = 34
17 x 2
17 x 2 = 34
3 6 4 8 6 12 10 20 18 36 34 68 Multiply 3 by 2 to get 6 Subtract 2 to get 4 Multiply 4 by 2 to get 8 Subtract 2 to get 6 Multiply 6 by 2 to get 12 Subtract 2 to get 10 .... Got it?
4005
1 x 34, 2 x 17.
The factors of 18 are: 1, 2, 3, 6, 9, 18 The factors of 34 are: 1, 2, 17, 34 The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
Well, honey, if you're looking to crack the code of 34, you're gonna need to multiply 1 by 34 or 2 by 17. That's the tea, darling. So, take your pick and go forth with your newfound mathematical wisdom.
2*17
The GCF is 2.