GMAT GYM - Prime Factorisation
The purpose of this exercise is to express the number with which you are presented as a product of prime numbers.
This exercise will include all numbers less than 1000 that can be expressed as a product of the prime numbers less than 30.
You may find it useful to familiarize yourself with the following common prime factorizations.
For example, the number 350 can be expressed as 2 X 52 X 7.
| 1024=210 | 729=36 | 625=54 | 343=73 |
| 512=29 | 243=35 | 125=53 | 49=72 |
| 256=28 | 81=34 | 25=52 | 7=71 |
| 128=27 | 27=33 | 5=51 |
| 64=26 | 9=31 |
| 32=25 | 3=31 |
| 16=24 |
Prime factorization is useful in conjunction with the Fundamental Theorem of Arithmetic, which states that “All integers greater than 1 can be expressed as the unique product of prime numbers."
e.g.
If a, b, and c are prime numbers and ab2c3= 3500, what is the value a + b - c?
To solve this problem, we can prime factor 3500 - 3500=225371
By substitution we get ab2c3=225371
So a=7, b=2, and c=5, and a + b – c =7 + 2 – 5, which equals 4.
Prime factorization can not only be useful on GMAT questions that test number property concepts such as factors, multiples, and prime numbers, but also on question that test arithmetic concepts such as multiplication, division, and powers.
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