Jane's Ice Cream Shoppe has 33 ice cream flavors, 5 syrups, and 11 toppings. How many different ways can you construct a sundae
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Answer:
28
Step-by-step explanation:
Any whole number can be broken down into its <em>prime factorization</em>, a product of all the prime number factors of a number. We can use a diagram called a <em>factor tree </em>to break numbers down into those factors. I've attached an image with the factor trees of 84 and 56 so you can see this process; 84 breaks down into 2 × 2 × 3 × 7, and 56 is 2 × 2 × 2 × 7. We can find the greatest common factor of these numbers by collecting all the prime factors they have in common and multiplying them together. 84 and 56 have 2, 2, and 7 in common, so their greatest common factor is 2 × 2 × 7 = 28
