Find the odd number out in the sequence: 396, 462, 572, 427, 671, 264.

Problem restatement
Among 396, 462, 572, 427, 671, 264, select the number that does not share the principal divisibility property of the rest.

Given data

• Sequence: 396, 462, 572, 427, 671, 264

Concept / Approach
Test for a strong common factor. A quick check shows many are divisible by 11. Use the 11-divisibility rule or direct division.

Step-by-step validation
396 ÷ 11 = 36 exactly (divisible by 11) 462 ÷ 11 = 42 exactly (divisible by 11) 572 ÷ 11 = 52 exactly (divisible by 11) 427 ÷ 11 = 38 remainder 9 (not divisible by 11) 671 ÷ 11 = 61 exactly (divisible by 11) 264 ÷ 11 = 24 exactly (divisible by 11)

All listed numbers are multiples of 11 except 427.

Verification / Alternative
11-rule: Alternating sum of digits is a multiple of 11.
396: (3 − 9 + 6) = 0 → divisible 462: (4 − 6 + 2) = 0 → divisible 572: (5 − 7 + 2) = 0 → divisible 427: (4 − 2 + 7) = 9 → not divisible 671: (6 − 7 + 1) = 0 → divisible 264: (2 − 6 + 4) = 0 → divisible

Common pitfalls

• Using only divisibility by 3: that splits the set but does not produce a unique outlier.

Final Answer
427