Break any number into primes, and see why there is only one way to do it. Then use the primes to find the HCF and the LCM, and solve real problems with them: bells that ring together, the largest tile for a floor, and buses that meet again.
3 lessons, about 1 h 25 min3 simulations11 problems6 practice questionsPython in every lesson
Created by StemPy LabEvery whole number greater than 1 is a prime or a product of primes. A factor tree or repeated division finds them. The Fundamental Theorem of Arithmetic says that there is exactly one such product, apart from the order. That is why a power of 6 can never end in 0.
The HCF of two or more numbers takes each common prime with its smallest power. The LCM takes every prime with its greatest power. For two numbers, HCF times LCM equals the product of the numbers. This rule does not hold for three numbers.
Word problems about the largest equal pieces need the HCF. Problems about things that happen together again need the LCM. A remainder changes the numbers first. For big numbers, Euclid's division method finds the HCF quickly, and so does Python's math.gcd.
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