Is-there-a-special-rule-for-divisibility-of-four-digit-numbers-by-13-

Question Number 211122 by hardmath last updated on 28/Aug/24

Is there a special rule for divisibility of four-digit numbers by 13?

Answered by mahdipoor last updated on 28/Aug/24

a b c d \equiv 0 (m o d 13)

\Rightarrow 1000 a + 100 b + 10 c + d \equiv 0

\Rightarrow - a - 4 b - 3 c + d \equiv 0

\Rightarrow a + 4 b + 3 c - d \equiv 0

a b c d \Rightarrow i f 13 ∣ (a + 4 b + 3 c - d) \Rightarrow 13 ∣ a b c d

f o r e x a m p l e :

1313 \Rightarrow 13 ∣ 1 + 4 (3) + 3 (1) - 3 = 13

6643 \Rightarrow 13 ∣ 6 + 4 (6) + 3 (4) - 3 = 39

a n d e c t \dots