Pregunta
Find the HCF of the following numbers: \( 20 ; 32 \); and 48
Ask by Reese Hanson. in South Africa
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The HCF of 20, 32, and 48 is 4.
Solución
1. Write the prime factorization of each number:
- \(20 = 2^2 \times 5\)
- \(32 = 2^5\)
- \(48 = 2^4 \times 3\)
2. Identify the common prime factors across all numbers.
The only common prime factor is \(2\).
3. Choose the smallest exponent of \(2\) found in the factorizations.
The exponents are:
- \(2^2\) in \(20\)
- \(2^5\) in \(32\)
- \(2^4\) in \(48\)
The smallest exponent is \(2\), so the factor is \(2^2\).
4. Therefore, the Highest Common Factor (HCF) is:
\[
2^2 = 4
\]
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Como
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Mind Expander
To find the HCF (Highest Common Factor) of 20, 32, and 48, let's break it down. First, we can find the prime factorization of each number: - 20 = 2^2 × 5 - 32 = 2^5 - 48 = 2^4 × 3 Next, identify the common factors. Here, the only common prime factor is 2, and the smallest exponent among these is 2 (from 20). So, the HCF = 2^2 = 4. Therefore, the HCF of 20, 32, and 48 is 4!

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