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Q: What do divisor multiple and factor have in common?

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No. Divisor is the same as factor.

A product (multiple) is divisible by a factor (divisor)

Because divisor is a synonym for factor.

"Factor" and "Divisor" are synonyms.

A factor or a divisor.

Factor and divisor are synonyms in this context.

the greatest common divisor or factor is 11

The least common factor of any set of positive integers is 1. The greatest common multiple is an infinite amount and not very practical.

The greatest common divisor (gcd) = 3. This is probably what you mean. Otherwise, the lowest common multiple (lcm) = 168.

divisor

1 is their Highest Common Factor or Greatest Common Divisor.

Divisor is another word for factor. Common divisors are often called common factors, in fact the term GCD or greatest common divisor is the same as GCF which is greatest common factor.

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