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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.
The largest of those numbers is the largest prime factor.
If you know what a factor tree is then it is the largest prime number that appears at the end of a branch.
If you do not know what a factor tree is: Try to factorise the number by every Prime number, starting from 2. If you find a factor make a note of it and divide the number that you are trying to factorise by the factor that you have just found. This quotient is the new number that you need to find the largest prime factor for. Start with the prime factor that you found at the last step and continue looking for factors until you reach the square root of the number.
If you have found any factors then the largest of them is the largest prime factor. If you have not, then the number is itself prime and so its largest prime factor is itself.
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