Originally coins were different colors because they were made of different metals whose cost reflected the coins' denominations. A cent (penny) was made of copper because copper was an inexpensive material and 1 cent worth of it could be made into a convenient-sized coin. Higher-value coins were made of nickel, silver, or gold in amounts equal to their denomination; e.g. a quarter contained 25¢ worth of silver, an eagle contained $10 in gold, and so on.
Modern US Coins are generally the same size and similar weight to their precious- metal ancestors so similar-color metals are used for consistency. Pennies are now made of zinc but are plated with copper; dimes, quarters, and halves are made of a cupronickel alloy that's similar in color to silver; $1 coins are struck in a brass alloy that resembles gold.
Many other countries take a somewhat different approach. Older denominations and sizes were replaced with new coins that are more practical for modern needs such as vending machines and coin-counters. Different colors are used to make it easy for people to identify the coins even if they have similar sizes and/or designs. In most cases the same relation of color to value is still used: low-value coins are copper-colored, medium-value coins are silver-colored, and higher-value coins are gold-colored. Many countries also use "ringed" coins, where an outer ring of one color surrounds a core piece of a different color.
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