1. Find Prime factorization of 72 using the Ladder method
Solution:
Prime factorization of a number using the Ladder method :
Step-1: Divide the number by the least prime number
Step-2: Continue dividing by that prime until it no longer divides evenly
Step-3: Divide by the next prime until it no longer divides evenly.
Step-4: Continue until the quotient is a prime.
Step-5: Write product of all the primes on the sides and top of the ladder.
The ladder method is also called stacked division method
To start building the ladder, divide 72 by the least prime number, which is 2
To add a step to the ladder, again divide 36 by the least prime number, which is again 2
To add a step to the ladder, again divide 18 by the least prime number, which is again 2
To add a step to the ladder, again divide 9 by the least prime number, which is 3
The quotient 3 is prime, so the ladder is complete and we stop here
The prime factorization is the product of all the primes on the sides and top of the ladder
`72=2 xx 2 xx 2 xx 3 xx 3`
We can write prime factorization in exponential form
`72=2^3 xx 3^2`
This material is intended as a summary. Use your textbook for detail explanation.
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