Question

Which is the LARGEST number that divides all of 12, 90 and 150?​

Answer 1

Answer:

Look at the prime factorizations of the numbers:

60 = 2 * 2 * 3 * 5

75 = 3 * 5 * 5

90 = 2 * 3 * 3 * 5

If you think about it, you’ll see that the gcd of those three numbers is 3 * 5, i.e. 15. Each of 60, 75, and 90 has 3 and 5 as a prime factor, and for each of 3 and 5, at least one of the numbers only has one 3 or one 5 as a factor.

(That’s not the only way to go. You can apply Euclid’s gcd algorithm to two of the numbers, and then again to the result and the third number.)

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