Question

29,618 Learners found this answer helpful

the greatest common factor (gcf) of two integers is 16.

which two integers share the gcf of 16?

select one answer
a 16, 36
b 32, 60
c 48, 96
d 48, 64

Explanation:

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<reasoning>

Understand the GCF definition

The Greatest Common Factor (GCF) is the largest positive integer that divides both numbers without leaving a remainder.

Analyze Option A

Check the factors of \(16\) and \(36\).
The factors of \(16\) are \(1, 2, 4, 8, 16\).
The factors of \(36\) are \(1, 2, 3, 4, 6, 9, 12, 18, 36\).
The common factors are \(1, 2, 4\).
The GCF is \(4\).

Analyze Option B

Check the factors of \(32\) and \(60\).
The factors of \(32\) are \(1, 2, 4, 8, 16, 32\).
The factors of \(60\) are \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\).
The common factors are \(1, 2, 4\).
The GCF is \(4\).

Analyze Option C

Check the factors of \(48\) and \(96\).
Since \(96 = 2 \times 48\), \(48\) is a factor of \(96\).
The GCF of \(48\) and \(96\) is \(48\).

Analyze Option D

Check the factors of \(48\) and \(64\).
The factors of \(48\) are \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\).
The factors of \(64\) are \(1, 2, 4, 8, 16, 32, 64\).
The common factors are \(1, 2, 4, 8, 16\).
The GCF is \(16\).
</reasoning>

<answer>
<mcq-option>(A) 16, 36</mcq-option>
<mcq-option>(B) 32, 60</mcq-option>
<mcq-option>(C) 48, 96</mcq-option>
<mcq-correct>(D) 48, 64</mcq-correct>
</answer>

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Answer:

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<reasoning>

Understand the GCF definition

The Greatest Common Factor (GCF) is the largest positive integer that divides both numbers without leaving a remainder.

Analyze Option A

Check the factors of \(16\) and \(36\).
The factors of \(16\) are \(1, 2, 4, 8, 16\).
The factors of \(36\) are \(1, 2, 3, 4, 6, 9, 12, 18, 36\).
The common factors are \(1, 2, 4\).
The GCF is \(4\).

Analyze Option B

Check the factors of \(32\) and \(60\).
The factors of \(32\) are \(1, 2, 4, 8, 16, 32\).
The factors of \(60\) are \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\).
The common factors are \(1, 2, 4\).
The GCF is \(4\).

Analyze Option C

Check the factors of \(48\) and \(96\).
Since \(96 = 2 \times 48\), \(48\) is a factor of \(96\).
The GCF of \(48\) and \(96\) is \(48\).

Analyze Option D

Check the factors of \(48\) and \(64\).
The factors of \(48\) are \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\).
The factors of \(64\) are \(1, 2, 4, 8, 16, 32, 64\).
The common factors are \(1, 2, 4, 8, 16\).
The GCF is \(16\).
</reasoning>

<answer>
<mcq-option>(A) 16, 36</mcq-option>
<mcq-option>(B) 32, 60</mcq-option>
<mcq-option>(C) 48, 96</mcq-option>
<mcq-correct>(D) 48, 64</mcq-correct>
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