Question 11

The smallest number of 4-digits leaving a remainder of 1 when divided by 2 or 3 or 4 or 6 has

Name: The smallest number of 4-digits leaving a remainder of 1 when divided by 2 or 3 or 4 or 6 has
Uploaded: 2026-08-08T14:19:12.087530+05:30
Duration: 3 min 42 s
Description: The smallest number of 4-digits leaving a remainder of 1 when divided by 2 or 3 or 4 or 6 has

Solution

A number leaving remainder 1 on division by 2, 3, 4, 5 and 6 is of the form $$60k + 1$$, because the LCM of these divisors is 60. The smallest 4-digit number of this form is $$60 \times 17 + 1 = 1021$$. Its digits are 1, 0, 2 and 1, so it contains only one zero.

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