1.3 Multiply by breaking the second number into its prime factors: \( 250 \times 240 \)
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To solve \( 250 \times 240 \) by breaking down the second number into its prime factors, we first factor \( 240 \) as \( 2^4 \times 3 \times 5 \). This means \( 240 = 16 \times 3 \times 5 \), resulting from \( 2 \times 2 \times 2 \times 2 \) and a \( 3 \) and \( 5 \). Now we can organize our calculations to get \( 250 \times 240 = 250 \times (2^4 \times 3 \times 5) \). Next, let's break down \( 250 \): it's \( 2 \times 5^3 \) (or \( 2 \times 125 \)). Combining the two, we rewrite the multiplication as \( (2 \times 5^3) \times (2^4 \times 3 \times 5) \). When we rearrange and regroup the multiplication, we find \( = 2^5 \times 3 \times 5^4 \). Crunching these numbers together, we discover \( 250 \times 240 = 60,000 \). This is not just a math trick; prime factorization is like assembling LEGO blocks, and knowing those little pieces makes multiplying big numbers a breeze! Plus, imagine this in action: chefs use variations of these calculations when scaling recipes! If a chef knows how to cater for 150 guests today but suddenly needs to switch gears for 300 guests tomorrow, employing prime factorization can quickly allow them to adjust ingredient quantities without breaking a sweat.
