"Calculate the remainder after dividing 31079 into 170166719."

After dividing land into three parts, you will have three pieces of land, I suppose. Why does dividing 2 into 8 equal 4? How can you divide 31079 into 170166719, which is less than the former?

31079 %% 170166719
[1] 31079
170166719 %% 31079
[1] 9194

170166719 %/% 31079
[1] 5475

If you divide something into something else, the object of the action might be the first “something.” But if you divide 8 by 2, do you say that you divide 2 into 8? I wonder if the object of the verb “divide” is the number 2, which you cannot divide by the number 8. In that case, the remainder is 2.

“The district, at that time, was divided into five kingdoms.” This means that someone (king?) divided THE DISTRICT into five kingdoms. The result is that each kingdom is smaller than the whole district.
“Divide 2 into 8. = Divide 8 by 2.” ← I feel this is strange. I cannot understand the logic behind this equation.

“Divide 2 into 8” =/= “Divide 8 by 2.”

I doubt people say “divide 2 into 8” to mean “divide 8 by 2”.
(I’m not sure if they did long time ago when mathematics wasn’t widely taught in school)

“divide 2 into 8” is counter-intuitive with the common expression “divide (sth) in / into half” or “cut (sth) in / into two”.
The target (object) of division comes before in/into, and either the divisor(two) or quotient(half) after.
“divide 2 into 8” means creating 8 parts in the result, which is not meant by “divide 8 by 2”.


“Calculate the remainder after dividing 31079 into 170166719.”
W. John Braun and Duncan J. Murdoch, A FIRST COURSE IN STATISTICAL PROGRAMMING WITH R, Cambridge University Press, 2007. p. 20.

170166719 / 31079 = 5475 … the remainder = 9194
I think that the answer is 9194.

I see.

So he’s using “divide X into Y” to mean “find out how many X’s fit into Y” or “how many X’s are in Y” - a different sense of “into”.

Well at first I thought it is not a common usage, but what a big surprise!

Apparently, this is a rather common usage too. For example there is at least one dictionary that lists it (DIVIDE INTO (phrasal verb) American English definition and synonyms | Macmillan Dictionary).

  • divide something into something to do a mathematical calculation to find out how many times a smaller number will fit into a larger number
  • Divide 3 into 9.

Also, google search returns many entries that discusses confusion about this usage. It does seem to confuse people, like you and me :slight_smile:

I wasn’t familiar with it.
I usually do a search before I answer something but not this time, and that’s when it gets you :slight_smile:

So the lesson is: Don’t overestimate your own knowledge; search engines are your best friend.

1 Like

Thank you for your comment, Userstk.

1 Like

Well, I thank you. I learned something too.

Divide two into four and Divide two by four
“Why does ‘divide two into four’ equal two, and ‘divide two by four’ equal one half?”

I remember this (eg. divide 2 into 4) as simply an old-fashioned idiomatic expression to say 4 divided by 2…
“How many times does 2 go into 4?” is the same sort of thing - which I still mentally think of when I do long-division/fractions by hand.

So 4÷2=2 [edited because it’s 1 am, lol]
But 2÷4=½

“Divide 31079 into 170166719” = 5475.3

1 Like

Dividing fractions can be a little tricky, that is multiply the number by the reciprocal of the fraction. More about…