Index form means using exponents.
Exponents are just a way of notating repeated factors.
The prime factorization of 72 is 2 x 2 x 2 x 3 x 3
The prime factorization of 72 is 2^3 x 3^2
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4623x2Since 2 is a prime number and so is 23 we can go no further.If 23 could be factored, we would put its factors on the next line. We would keep going until we had all primes. It is not possible to write it in tree form here, so we left justify it.
Put the factors of one number in the left circle and the factors of the other in the right circle. Put any common factors in the middle where the circles intersect. The largest of these is the GCF.
The factors of 3 are 1 and 3. Put three blocks in one row.
There cannot be a greatest common factor of just one number. To be common there need to be at least two numbers. If you find all the factors of two or more numbers, and you find some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
List the number at the bottom. Break it down into factors by placing them on successive lines above the original number. Stop when all the factors are prime. 7,5,3,2 35,3,2 105,2 210