Question

Find the HCF of 24,52 and
100 using prime factorization method.​

Answer 1

Answer:

4

Step-by-step explanation:

as we know in  prime factorization method hcf is the product of all the common prime factors of given no.

prime factorization of 24=2*2*2*3

prime factorization of 52=2*2*13

prime factorization of 100=2*2*5*5

common prime factors in all=2*2

so hcf=2*2=4

Answer 2

STEP 1:

Find the prime factor of each number -

★ Prime factor of 24

$\begin{array}{r | l}</p><p>2 & 24 \\</p><p> \cline{2-2} 2 & 12 \\</p><p> \cline{2-2} 2 & 6 \\</p><p> \cline{2-2} 3 & 3 \\</p><p> \cline{2-2} & 1</p><p> \end{array}$

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★ Prime factor of 52

$\begin{array}{r | l}</p><p>2 & 52 \\</p><p> \cline{2-2} 2 & 26 \\</p><p> \cline{2-2} 13 & 13 \\</p><p> \cline{2-2} & 1</p><p> \end{array}$

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★ Prime factor of 100

$\begin{array}{r | l}</p><p>2 & 100 \\</p><p> \cline{2-2} 2 & 50 \\</p><p> \cline{2-2} 5 & 25 \\</p><p> \cline{2-2} 5 & 5 \\</p><p> \cline{2-2} & 1</p><p> \end{array}$

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STEP 2:

Express the prime factor of each number. Choose the common numbers from all sets.

• Prime Factor of 24 = ${\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times 3$

• Prime Factor of 52 = ${\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times 13$

• Prime Factor of 100 = ${\boxed{\sf{\pink{2}}}} \times {\boxed{\sf{\purple{2}}}} \times 5 \times 5$

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STEP 3:

Get the product of these chosen comman factors to find the HCF.

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$:\implies\sf 2 \times 2$

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$:\implies\bf \blue{4}$

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$\therefore\sf\; \underline{Hence,\;the\;HCF\;of\;24,\;52\;and\;100\;is\;\bf{4}.}$