divisor / factor
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factor / divisor
In mathematics, a whole number by which another whole number can be divided without a remainder.
Die Zahl 4 ist ein Teiler von 12, weil 12 geteilt durch 4 gleich 3 ist.
The number 4 is a factor of 12 because 12 divided by 4 equals 3.
'Teiler' (divisor/factor) is derived from the verb 'teilen' (to divide/share). The ending '-er' turns the verb into a noun that describes the person or thing performing the action. So a Teiler is literally 'something that divides.'
Wenn man eine Zahl teilt, braucht man immer einen Teiler.
When you divide a number, you always need a divisor.
The word 'Teiler' (divisor/factor) is used almost exclusively in a mathematical context. It is rarely used in everyday conversation.
Im Mathematikunterricht lernen wir heute, was ein Teiler ist.
In math class today, we're learning what a divisor is.
When one number divides another without a remainder, the preposition 'von' (of) is used. When describing a division problem, 'Teiler' often appears without a preposition as the name for a position in the calculation.
Die Zahl 7 ist ein Teiler von 49.
The number 7 is a factor of 49.
A very common and important combination in mathematics is 'größter gemeinsamer Teiler' (greatest common divisor), often abbreviated as 'ggT' in German. It is the largest factor that two or more numbers have in common.
Der größte gemeinsame Teiler von 12 und 18 ist 6.
The greatest common divisor of 12 and 18 is 6.
factor
'der Faktor' and 'der Teiler' both belong to mathematics and have to do with numbers. A factor is a number in a multiplication; for example, in 3 times 4, 3 and 4 are factors. A divisor is a number by which another number can be divided without a remainder, or the number by which you divide in a division problem. The words can be confusing because the same number can be both in different problems. So the difference depends on the type of calculation: with multiplication you use factors, and with division you use a divisor.
Im Matheheft markiert Julian alle Teiler von 24.
In his math notebook, Julian marks all the divisors of 24.
In der Aufgabe 6 mal 5 ist 6 ein Faktor.
In the problem 6 times 5, 6 is a factor.