Answer :

The highest common factor of 330 and 396 using prime factorization is 66.

To find the highest common factor (HCF) of 330 and 396 using prime factorization, we'll first break down each number into its prime factors, and then identify the common prime factors along with their lowest powers.

Step 1: Prime Factorization of 330

330 can be expressed as:

[tex]\[330 = 2 \times 165\][/tex]

[tex]\[= 2 \times 3 \times 55\][/tex]

[tex]\[= 2 \times 3 \times 5 \times 11\][/tex]

Step 2: Prime Factorization of 396

396 can be expressed as:

[tex]\[396 = 2 \times 198\][/tex]

[tex]\[= 2 \times 2 \times 99\][/tex]

[tex]\[= 2 \times 2 \times 3 \times 33\][/tex]

[tex]\[= 2 \times 2 \times 3 \times 3 \times 11\][/tex]

Step 3: Identify Common Prime Factors

The common prime factors between 330 and 396 are 2, 3, and 11.

Step 4: Find the Lowest Power of Common Prime Factors

For 2: It appears in both prime factorizations as [tex]\(2^1\)[/tex].

For 3: It appears in both prime factorizations as [tex]\(3^1\)[/tex].

For 11: It appears in both prime factorizations as [tex]\(11^1\)[/tex].

Step 5: Multiply the Lowest Powers of Common Prime Factors

[tex]\[HCF(330, 396) = 2^1 \times 3^1 \times 11^1\][/tex]

[tex]\[= 2 \times 3 \times 11\][/tex]

[tex]\[= 66\][/tex]

Therefore, the highest common factor of 330 and 396 is 66.

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Rewritten by : Jeany

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