666 is 111 multiplied by 6, 111 in turn is semisimple number: 111 = 37*3.
407 cannot be divided by 3, cause 4+0+7 =11, thus we check 407 whether it can be divided by 37, and here we are, 37*11=407, Thus 407/666= 11/18.
Even simler approach: if this fraction can be simplified at all, 407 must contain at least one of these primes 2, 3, 37 as multiplier (666= 2*3*3*37).
For obvious reasons we must exclude 2, 3 and its combinations, that left us with the only candidate - 37
Side note: we can solve this even faster using notion of cyclotomic polynomial and repunits.
2026-04-26 22:09:01
1
Earl :
All's good....but dividing 666 by 37 is still equally difficult
2026-04-24 07:21:22
1
jay :
since you had to use a calculator to find the answer of 666÷37 and 407÷37, you might as well save yourself all that trouble by using the calculator from the beginning to find the answer in one step
2026-05-08 04:49:32
2
Manullang :
I am late to know this trik
2026-04-24 10:53:50
3
Mr Dee :
let me try it
2026-06-19 15:27:09
1
a :
thank you
2026-04-23 08:00:22
1
user075604989 :
Was anyone else subtracting that fast?
2026-04-22 20:42:42
2
Sadia Zaker :
You talk too much!
2026-06-08 03:23:11
2
Joona🇫🇮⚛️ :
Just use greatest common divisor or euclidean algorithm
2026-04-22 17:42:39
5
Me 1 :
and you know 666÷37 how ?
same why ?
sounds long
before calculators I used trig tables and log books.
I no longer do that ... I use a calculator...
so ...
2026-05-28 11:56:48
1
BlossomintoLight :
Getting an understanding 😊👍
2026-05-31 02:07:47
1
Trufflepesto and 307 others :
My great grandfather invented this technique 👍
2026-06-11 18:08:38
1
Quran and Hadith Bitesize :
Can’t simply
2026-05-13 05:07:47
1
the jetta family :
0.678
2026-05-26 10:52:25
0
michelsauve :
666 is 6x3x37. 407 not a multiple of the smaller factors, so it must be a multiple of 37. Yep. It’s 11/18. Done.