Real numbers
Grade Class 10
Question:
<p>HCF of (2<sup>3</sup> <span class="math-tex">\(\times\)</span> 3<sup>2</sup> <span class="math-tex">\(\times\)</span> 5), (2<sup>2</sup> <span class="math-tex">\(\times\)</span> 3<sup>3</sup> <span class="math-tex">\(\times\)</span>5<sup>2</sup>) and (2<sup>4</sup> <span class="math-tex">\(\times\)</span> 3<sup> </sup><span class="math-tex">\(\times\)</span> 5<sup>3</sup> <span class="math-tex">\(\times\)</span> 7) is</p>
<p style="display:inline">105</p>
<p style="display:inline">30</p>
<p style="display:inline">60</p>
<p style="display:inline">48</p>
Step-by-Step Solution
Key Concept: To find the HCF of expressions in prime factorization form, take the product of the lowest power of each prime factor that is common to all expressions.
<p>HCF = (2<sup>3</sup> <span class="math-tex">\(\times\)</span> 3<sup>2</sup> <span class="math-tex">\(\times\)</span> 5, 2<sup>2</sup> <span class="math-tex">\(\times\)</span> 3<sup>3</sup> <span class="math-tex">\(\times\)</span> 5<sup>2</sup>, 2<sup>4</sup> <span class="math-tex">\(\times\)</span> 3 <span class="math-tex">\(\times\)</span> 5<sup>3</sup> <span class="math-tex">\(\times\)</span> 7)<br />
HCF = Product of smallest power of each common prime factor in the numbers<br />
= 2<sup>2</sup> <span class="math-tex">\(\times\)</span> 3 <span class="math-tex">\(\times\)</span> 5 = 60</p>
Correct Answer: C