The factorisation of number may not be unique but it prime factorisati...
Factorisation of the Smallest 3-Digit Number
Factors are numbers that can be multiplied together to get another number. The factorisation of a number is the expression of that number as a product of its factors. The factorisation of a number may not be unique, but its prime factorisation is unique.
Smallest 3-Digit Number: 100
When we consider the smallest 3-digit number, which is 100, we can find its factorisation as follows:
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factorisation of 100: 1 x 100, 2 x 50, 4 x 25, 5 x 20, 10 x 10
Prime Factorisation of 100
To find the prime factorisation of 100, we need to express it as a product of prime numbers:
100 = 2 x 2 x 5 x 5 = 2^2 x 5^2
The prime factorisation of 100 is unique, as it can only be expressed as 2^2 x 5^2. This means that no matter how we factorise 100 into its prime factors, we will always end up with 2^2 x 5^2.
Therefore, the factorisation of a number may vary, but its prime factorisation is always unique.
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