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Subjects>Math>Other Math

Is the divides relation on the set of positive integers transitive?

Anonymous

∙ 13y ago

Updated: 4/28/2022

Yes.

Suppose x divides y then there exist an integer p such that y = px.

Suppose y divides z then there exist an integer q such that z = qy.

Therefore z = q*px = qp*x

Since p and q are integers then pq is an integer and therefore x divides z.

That is to say: if x divides y and y divides z, then x divides z.

Wiki User

∙ 13y ago

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Q: Is the divides relation on the set of positive integers transitive?

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Is the divides relation on the set of positive integers antisymmetric?

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Related Questions

Is the divides relation on the set of positive integers is reflexive?

No, it is not.

Is the divides relation on the set of positive integers antisymmetric?

No it is not.

Is the divides relation on the set of positive integers symmetric?

No, it is not.

Is mean another way to say positive number?

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If 42 divides n what are other positive integers that divide n?

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Multiplying and dividing integers is real easy. All you have to do is do regular dividing and multiplying keeping in mind these simple rules: RULES: 1: When multiplying or dividing integers, when the numbers are a positive, positive they equal a positive. When the numbers are negative, negative they equal a positive. In other words, same signs equal positive. 2: This rule is very similar to the rule above. The only change is that when the signs are different, they equal a negative. ( negative, positive= negative, positive, negative= negative.) Please correct me if I'm wrong. Multiply integers- my notes from class positive x positive= positive positive x negative= negative negative x negative= positive Divide integers- again my notes from class positive divided by a positive= positive negative divided by a negative= positive negative divided by a positive= negative Dividing integers are simple if the number has a different sign than the other it is always negative but if they have the same sign its always positive ex. -20/5=-4 ex. -20/-4=-5

Define greatest common factor?

In math, the greatest common factor (GCF) of two or more non-zero integers is the largest positive integer that divides the numbers without a remainder.

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In math, the greatest common divisor (GCD) of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

Why is 147 a factor?

Any positive integer, k, is a factor because it will divide larger integers of the form 2k, 3k etc. 147 divides 294, for example and so is a factor of 294.

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Cannot be answered because in math, the greatest common divisor (GCD) of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

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