Arithmetic

Counting Divisors of a Number

How many divisors (also called factors) does a number have? We’ve answered many questions about that over the years, sometimes by just guiding a student to discover it, sometimes either deriving the formula for them or just showing and using it. Let’s look at a few. Discovering the trick We’ll start with a question from …

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Leap Years: When and Why

Last week we looked at some questions that arose leading up to the year 2000, triggered by the 20th anniversary of that event. Now we’ll start from a different question about that year, to look at the story of leap years. Was 2000 a leap year, or not? Here is the question from 1999: Year …

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2020 and the Y0K Problem

The arrival of 2020 has brought to mind the various controversies at the start of the year 2000, also called Y2K. As a software engineer responsible for date-sensitive communications within large computer systems, I well recall being on call that Saturday, in case something went wrong. I also recall all the questions we got in …

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One More Way to Find GCF and LCM

There are so many ways to find a Least Common Multiple that I had to omit one method we have been asked about several times. This one doesn’t require finding prime factors, but focuses on division by whatever factors you see. Divide everything by whatever works The first reference to the method I have found …

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How Do You Simplify a Fraction?

Last time we examined the basic concept of equivalent fractions – the fact that different fractions can represent the same value. We saw that there will be one way to write a fraction that is “in lowest terms” – no other fraction with the same value will involve smaller numbers, and all the others can …

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