Real numbers
Grade Class 10
Question:
<p>If a = (2<sup>2</sup> <span class="math-tex">\(\times\)</span> 3<sup>3</sup> <span class="math-tex">\(\times\)</span> 5<sup>4</sup>) and b = (2<sup>3</sup> <span class="math-tex">\(\times\)</span> 3<sup>2</sup> <span class="math-tex">\(\times\)</span> 5) then HCF (a, b) = ?</p>
<p style="display:inline">540</p>
<p style="display:inline">360</p>
<p style="display:inline">180</p>
<p style="display:inline">90</p>
Step-by-Step Solution
Key Concept: The HCF of numbers expressed in prime factorization is calculated by taking the product of the lowest powers of all common prime factors.
<p>It is given that: a = (2<sup>2</sup> <span class="math-tex">\(\times\)</span> 3<sup>3</sup> <span class="math-tex">\(\times\)</span> 5<sup>4</sup>) and b = (2<sup>3</sup> <span class="math-tex">\(\times\)</span> 3<sup>2</sup> <span class="math-tex">\(\times\)</span> 5)<br />
<span class="math-tex">\(\therefore\)</span> HCF (a, b) = Product of smallest power of each common prime factor in the numbers = 2<sup>2</sup> <span class="math-tex">\(\times\)</span> 3<sup>2</sup> <span class="math-tex">\(\times\)</span> 5 = 180</p>
Correct Answer: C