# What Is the Definition of Decomposing Numbers?

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In mathematics, "decomposing numbers" is a term with a very specific definition. Learn about the definition of decomposing numbers with help from a longtime math teacher in this free video clip.

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## Video Transcript

Hi my name is Marija, I'm a mathematician and today I'm going to tell you the definition of decomposing a number. So if you're in the lower grades, what they mean by decompose a number is to break it up into its value. So if I have the number 35, the elementary grades might decompose this by showing the value of the three as being in the tens place so they would write out 30 plus five is in the ones place so we would just write that as five. But if you're in middle school or high school, what you probably mean by the decomposition of a number is to break it down into its prime factors. So if I want to take the number 24 and decompose it, what I would do is do a factor tree. So I'm going to break 24 down into two factors, any that come to mind, and for me those numbers are 12 and 2. And every time I see a prime number when I start to break it down I'm going to circle that number. And I'm going to continue to break down the other branches. So 12 will be broken down into six and two, and I'm going to circle this two as well. And six will be broken down into three times two and both of these will be circled because they're both prime. So now that I've circled all of my branches, I'm going to go ahead and write it out as two times two times two times three or because there's three twos being multiplied that can be written as two to the third power times three, and this would be the decomposition of the number 24. My name is Marija and I just told you how to decompose a number.

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