Q: What is the term for a fraction when the denominator and numerator do not have any more factors in common?

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If a fraction's numerator and denominator have no factors other than one in common, the fraction cannot be simplified except if the denominator is 1, in which case the fraction can be simplified to the whole number of the numerator.

If the numerator and denominator of a fraction have a common factor (except for '1'), divide both numerator and denominator by their common factor. The fraction is in the simplest form when the numerator and denominator have no common factors.

You search for common factors in the numerator and the denominator. Then you divide numerator and denominator by this common fraction. For example, in the fraction 9/12, the common factor is 3. If you divide numerator and denominator (top and bottom) by 3, you get 3/4, which is an equivalent fraction.

A fraction is considered simplified or reduced when the numerator and denominator have no common factors other than 1. In other words, there is no integer greater than 1 that divides evenly into both the numerator and the denominator. If there are common factors, the fraction can be simplified further by dividing both the numerator and denominator by their greatest common factor.

Where the numerator and denominator have no further common factors

Related questions

If a fraction's numerator and denominator have no factors other than one in common, the fraction cannot be simplified except if the denominator is 1, in which case the fraction can be simplified to the whole number of the numerator.

If the numerator and denominator are prime numbers and not equal then they don't have common factors (except 1 which would be a common factor even if the numerator and denominator were prime numbers).

If the numerator and denominator of a fraction have a common factor (except for '1'), divide both numerator and denominator by their common factor. The fraction is in the simplest form when the numerator and denominator have no common factors.

You search for common factors in the numerator and the denominator. Then you divide numerator and denominator by this common fraction. For example, in the fraction 9/12, the common factor is 3. If you divide numerator and denominator (top and bottom) by 3, you get 3/4, which is an equivalent fraction.

A fraction is considered simplified or reduced when the numerator and denominator have no common factors other than 1. In other words, there is no integer greater than 1 that divides evenly into both the numerator and the denominator. If there are common factors, the fraction can be simplified further by dividing both the numerator and denominator by their greatest common factor.

Where the numerator and denominator have no further common factors

If the numerator and the denominator have no common factors other than one, the fraction is already in its simplest form.

That IS the reduced or simplified fraction.

yes

If the numerator and denominator have any common factors (other than 1), then both the numerator and denominator can be divided by the common factor, and the new fraction will be equivalent to the original fraction in reduced form.

Yes. If the numerator and denominator of a fraction are prime, the fraction is in simplest form. The reason is that each number has only two factors, 1 and the number itself. For that reason, it is not possible for the numerator and denominator to have any factors (other than 1) in common.

The fraction is in its simplest form.