Here's one mnemonic "Bright Boys Rave Over Young Girls But Veto Getting Wed. Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White <=> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Best method to memorize is - B.B. Roy of Great Britain Veto getting wed. Alternatively, most of the colors are those from the traditional rainbow. Black is 0 (as in 'nothing'), Brown is 1, then Red through Violet, and finally Gray and White are 8 and 9. In Russian language, you can use the following phrase: "Четыре коровы красят ржавый железный забор синтетической формулой, содержащей белок" - чёрный, коричневый, красный, рыжий, жёлтый, зелёный, синий, фиолетовый, серый, белый. By the way, the phrase is translated as "Four cows paint a rusty iron fence with a synthetic formula containing protein".
The multiplier band goes by the same code and can be read as "followed by N zeros", plus Gold for "divide by 10" and Silver for "divide by 100".
Tolerances are something of a mess: Brown and Red are 1% and 2% (you usually spot them because they have an extra significant digit), Gold and Silver are 5% and 10%, and 20% doesn't even get a tolerance band (you will rarely, if ever, come across one of these).
To read the whole thing, put the tolerance band at your right, and go like this: "green-brown-red-gold = 5-1-00-5% = 5.1K 5%". You'll get used soon enough, and a bit later you'll be spotting what you want at once. It's also easy to classify them by decade: red is Ks, orange is 10Ks ...
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