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Answer :
The highest common factor (HCF) of 308 and 330 is 11.
To find the highest common factor (HCF) of 308 and 330, we can use the method of prime factorization or the Euclidean algorithm. I will use the prime factorization method here.
Step 1: Prime Factorization
We need to find the prime factorization of both numbers.
Factorizing 308:
- Start with the smallest prime, which is 2:
308 ÷ 2 = 154 - Next, factor 154:
154 ÷ 2 = 77 - Now, factor 77:
77 ÷ 7 = 11 - Finally, 11 is a prime number.
So, the prime factorization of 308 is:
[tex]308 = 2^2 \times 7^1 \times 11^1[/tex]
Factorizing 330:
- Start with 2 again:
330 ÷ 2 = 165 - Next, factor 165 by checking 3 (sum of digits is divisible by 3):
165 ÷ 3 = 55 - Now, factor 55:
55 ÷ 5 = 11 - Finally, 11 is a prime number.
So, the prime factorization of 330 is:
[tex]330 = 2^1 \times 3^1 \times 5^1 \times 11^1[/tex]
Step 2: Identify the common factors
Now, let's identify the common prime factors between 308 and 330:
- The common prime factor is [tex]11[/tex].
Step 3: Calculate the HCF
To find the HCF, we take the lowest power of the common factors. In this case, the only common factor is 11, which is raised to the power of 1 in both factorizations. Hence, the HCF is:
[tex]HCF = 11^1 = 11[/tex]
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Rewritten by : Jeany
The highest common factor of 308 and 330 is 22
To find the highest common factor (HCF) of 308 and 330, we can use prime factorization.
Prime factors of 308:
308 = 2 × 2 × 7 × 11
Prime factors of 330:
330 = 2 × 3 × 5 × 11
308 and 330 share the prime factors 2 and 11.
The HCF is the product of the common prime factors
2 × 11 = 22
