Divisibility rule of 7

[finite cradle]

What is it can someone teach me the concept

[oak root]

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[finite cradle]

Like how do i know that a number is divisible by 7 or not

[calm lion]

give me a few minutes, i believe i have a divisibility rule

but it is a long process

[finite cradle]

No like for example there is a number 198402038 and i want to find out whether it is divisible by 7 so i would need the shortest way to do so

[calm lion]

oh...

well uh

[echo anchor]

hi

@finite cradle theres a rule

[finite cradle]

Ik

Yes

[echo anchor]

yes

you just remove the unit digit

[finite cradle]

What is it

[echo anchor]

double it

and subtract it from the rest of the number

[calm lion]

i was gonna tell hi

😦

[echo anchor]

so for example 5849303

58492-8

[finite cradle]

Like in 264 we will take 4 and double so now it is 8 and then subtract it from 264 , which is 264-8 = 256?

[echo anchor]

yes

no

wait

no

subtract it from 26

only

not 264

[finite cradle]

Ohk

[echo anchor]

26-8

thats

something

idk

,calc 26-8

[polar path]

Result:

18

[finite cradle]

So 184

[echo anchor]

18

not divisible by 7

[echo anchor]

why are u adding the 4 back

[finite cradle]

Got it

Subtract it from the first two digits?

[echo anchor]

in general

[finite cradle]

Lets try on this one maybe 3,04,248

,calc 30-16

[polar path]

Result:

14

[echo anchor]

for an $n$ digit number, you find twice the units digit and subtract it from the string of $n-1$ digits

[calm lion]

[polar path]

waffle

[finite cradle]

Divisible?

[echo anchor]

No??

Bruh

[echo anchor]

30424-16

[finite cradle]

Oh

From the rest of the digits got it

,calc 30424-16

[polar path]

Result:

30408

[echo anchor]

3040-16

,calc 3040-16

[polar path]

Result:

3024

[echo anchor]

302-8

,calc 302-8

[polar path]

Result:

294

[echo anchor]

,calc 29-8

[polar path]

Result:

21

[echo anchor]

divisible

,calc 304248/7

[polar path]

Result:

43464

[echo anchor]

integer

there

[finite cradle]

Yes nice

It is divisible

Correct

[finite cradle]

Does this rule work everytime

[echo anchor]

yea

i can prove the rule to u

[finite cradle]

Okk

[finite cradle]

Nono need

[echo anchor]

aight

[finite cradle]

Thanks for helping @echo anchor

[glad spire]

@finite cradle has given 1 rep to @echo anchor

[finite cradle]

+close