Henry Ernest Dudeney/Modern Puzzles/65 - Dividing by 37

Modern Puzzles by Henry Ernest Dudeney: $65$

Dividing by $37$

I want to know whether the number $49,129,308,213$ is exactly divisible by $37$,

or if not, what is the remainder when so divided.

How may I do this quite easily without any process of actual division whatever?

It can be done by inspection in a few seconds -- if you know how.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $65$. -- Dividing by $37$
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $116$. Dividing by $37$