Pregunta
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2.2. Write down: 2.2.1. the prime factors of 132 . 2.2 .2 . the HCF of 48 and 88 . 2.2 .3 . the LCM of 24 and 96 .

Ask by Howell Malone. in South Africa
Feb 26,2025

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- Prime factors of 132: 2, 2, 3, 11 - HCF of 48 and 88: 8 - LCM of 24 and 96: 96

Solución

2.2.1. Prime factors of 132:   132 can be broken down as follows:   132 = 2 × 66     = 2 × 2 × 33     = 2 × 2 × 3 × 11   Thus, the prime factors are 2, 2, 3, and 11 (or simply 2, 3, and 11 as the unique prime factors). 2.2.2. HCF (Highest Common Factor) of 48 and 88:   First, express each number in its prime factorization:   48 = 2⁴ × 3   88 = 2³ × 11   The common prime factors are with base 2. Take the smallest exponent:   HCF = 2³ = 8. 2.2.3. LCM (Least Common Multiple) of 24 and 96:   Write the factorizations:   24 = 2³ × 3   96 = 2⁵ × 3   For LCM, take the highest powers of all primes present:   LCM = 2⁵ × 3 = 32 × 3 = 96. Thus, the answers are:  • Prime factors of 132: 2, 2, 3, 11 (or 2, 3, and 11).  • HCF of 48 and 88: 8.  • LCM of 24 and 96: 96.

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Beyond the Answer

To break down 132, we find that its prime factors are 2, 3, and 11, giving us the expression 2 x 2 x 3 x 11 or \(2^2 \times 3 \times 11\). This means 132 can be vividly envisioned as a product of these building blocks! For the HCF (Highest Common Factor) of 48 and 88, we note that they share the factors of 1, 2, 4, and 8. Thus, the HCF is 8, making it the biggest number that divides both without leaving any remainder—a true best buddy among their factors! Lastly, the LCM (Lowest Common Multiple) of 24 and 96 is 96. This means 96 is the smallest number that can be divided evenly by both 24 and 96—like finding the first perfect meeting point in a friendship. So if you're looking for a common stage to showcase talents, that’s where it’s at!

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