No, it is not.
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If the last digit doubled subtracted from the rest is a multiple of 7, the whole number is divisible by 7. Example: 686 68 - 12 = 56 56 is divisible by 7. 686 is divisible by 7.
973 is divisible by: 1, 7, 139, 973.
Double the last digit, subtract it from the rest. If the result is divisible by 7, the whole number is divisible by 7.
If you double the last digit and subtract it from the rest of the number and the answer is zero or divisible by 7, then the whole number is divisible by 7.
When a number is a multiple of seven it is also divisible by seven.