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If the number(say 66317) is not divisible by 3, it will leave a modulo of either 0,1 or 2. If I decrease the number by 5, I am basically making it a multiple of 3, and the remaning digits will be a multiple of 5 as I am subtracting it from the number.
modulo 0 implies number divisibile modulo 1 implies 5 needs to be subtracted twice. modulo 2 implies 5 needs to be subtracted once.