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What is the Greatest Common Factor (GCF) of 25 x^2
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Updated on: 29 Apr 2026, 00:23
Updated on: 29 Apr 2026, 00:23
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Question Stats:
25% (00:56) correct
75% (00:18) wrong based on 4 sessions
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\(x\) and \(y\) are \(\neq 0\)
\(\text { What is the Greatest Common Factor (GCF) of } 25 x^2 \text { and } 16 y^4 \text { ? }\)
A. 0
B. 1
C. \(x y^2\)
D. \(x^2 y^4\)
E. \(400 x^2 y^4\)
[/m]
\(\text { What is the Greatest Common Factor (GCF) of } 25 x^2 \text { and } 16 y^4 \text { ? }\)
A. 0
B. 1
C. \(x y^2\)
D. \(x^2 y^4\)
E. \(400 x^2 y^4\)
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Re: What is the Greatest Common Factor (GCF) of 25 x^2
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28 Apr 2026, 08:54
28 Apr 2026, 08:54
Expert Reply
Check for common factors across three dimensions:
Common factor.png [ 33.44 KiB | Viewed 510 times ]
Since 25 and 16 are coprime ( \(\operatorname{GCF}(25,16)=1\) ), and the variables x and y are entirely different with no overlap, there are no shared factors at all. When two expressions share no common factors other than 1, their GCF is 1 - which is always a trivial common factor of any two integers.
The other answer choices fail because: A (0) is never a GCF; C, D introduce variables not present in both terms; and E is actually the product \(25 \times 16 \times x^2 \times y^4\), which is the LCM-like combination, not the GCF.
Attachment:
Common factor.png [ 33.44 KiB | Viewed 510 times ]
Since 25 and 16 are coprime ( \(\operatorname{GCF}(25,16)=1\) ), and the variables x and y are entirely different with no overlap, there are no shared factors at all. When two expressions share no common factors other than 1, their GCF is 1 - which is always a trivial common factor of any two integers.
The other answer choices fail because: A (0) is never a GCF; C, D introduce variables not present in both terms; and E is actually the product \(25 \times 16 \times x^2 \times y^4\), which is the LCM-like combination, not the GCF.
gmatclubot
Re: What is the Greatest Common Factor (GCF) of 25 x^2 [#permalink]
28 Apr 2026, 08:54
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