Card 1 of 20
EasyStudy card 1
Prompt
What is a prime number?
Answer
A positive integer greater than \(1\) with exactly two positive factors: \(1\) and itself.
MathChapter 10: Law of Exponents and Polynomials
Flashcards
Prime Factorization, GCF, and LCM Flashcards
Recall prime structure, factor trees, minimum and maximum exponent rules, and verification checks.
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Card 2 of 20
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Prompt
Is \(1\) prime, composite, or neither?
Answer
Neither prime nor composite.
Card 3 of 20
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Prompt
When is a factor tree complete?
Answer
When every leaf is prime and every child pair multiplies to its parent.
Card 4 of 20
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Prompt
Can two correct factor trees start differently?
Answer
Yes. Their final multisets of prime leaves will still match.
Card 5 of 20
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Prompt
Write the prime factorization of \(72\).
Answer
\(2^3\cdot3^2\)
Card 6 of 20
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Prompt
Why is \(72=8\cdot9\) not a complete prime factorization?
Answer
Both \(8\) and \(9\) are composite.
Card 7 of 20
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Prompt
Which exponent of a shared prime belongs in the GCF?
Answer
The smallest exponent common to every expression.
Card 8 of 20
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Prompt
Which exponent of a prime belongs in the LCM?
Answer
The largest exponent required by any expression.
Card 9 of 20
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Prompt
Which prime bases belong in a GCF?
Answer
Only bases present in every expression.
Card 10 of 20
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Prompt
Which prime bases belong in an LCM?
Answer
Every base appearing in at least one expression.
Card 11 of 20
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Prompt
What divisibility check must a proposed GCF pass?
Answer
It must divide every input exactly.
Card 12 of 20
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Prompt
What divisibility check must a proposed LCM pass?
Answer
Every input must divide it exactly.
Card 13 of 20
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Prompt
Find \(\operatorname{GCF}(18,30)\).
Answer
\(6\)
Card 14 of 20
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Prompt
Find \(\operatorname{LCM}(18,30)\).
Answer
\(90\)
Card 15 of 20
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Prompt
What variable power belongs in the GCF of \(x^7\) and \(x^3\)?
Answer
\(x^3\)
Card 16 of 20
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Prompt
What variable power belongs in the LCM of \(y^4\) and \(y^9\)?
Answer
\(y^9\)
Card 17 of 20
HardStudy card 17
Prompt
What identity connects the GCF and LCM of two positive integers?
Answer
Their product equals the product of the two integers.
Formula
\[ab=\operatorname{GCF}(a,b)\operatorname{LCM}(a,b)\]
Card 18 of 20
MediumStudy card 18
Prompt
Why should \(1\) never appear as a prime factor?
Answer
It is not prime and adding it conveys no factor information.
Card 19 of 20
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Prompt
How do you factor a monomial completely?
Answer
Prime-factor the coefficient and write each variable as its powered prime-like factor inventory.
Card 20 of 20
MediumStudy card 20
Prompt
What quick phrase distinguishes GCF from LCM exponents?
Answer
GCF takes shared minimums; LCM takes all maximums.
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