All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
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83 is prime. No tree.
61 is already prime. It doesn't need a tree.
When the bottom branch consists entirely of prime numbers.
145 5,29 Not much of a tree. More like a factor shrub.
The purpose of a factor tree is to divide a number into prime factors. 1 is not a prime number.