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Every (a) number can be expressed (factorised) as the product of (b) factors and this factorisation is (c) except for the order in which the prime factor occur.
{Also explain why you filled the blank with the same}
Dear Student,
Every (a) composite number can be expressed (factorised) as the product of (b) prime factors and this factorisation is (c) unique except for the order in which the prime factors occur.
All composite numbers have a unique set of prime factors. For example, 15 = 3 x 5, 16 = 2 x 2 x 2 x 2, 18 = 3 x 3 x 2, etc. If, in the prime factorisation of 15, a 2 is multiplied to the prime factors, then, 3 x 5 x 2 = 30; which is another number, with a unique set of prime factors; 3, 5 and 2. Thus, on multiplication of 3 and 5, we can only get 15, making the prime factorisation unique. However, since the order in which numbers are multiplied doesn't matter, or 3 x 5 = 5 x 3 = 15; thus, the factorisation is unique, except for the order in which the prime factors occur.
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Every (a) composite number can be expressed (factorised) as the product of (b) prime factors and this factorisation is (c) unique except for the order in which the prime factors occur.
All composite numbers have a unique set of prime factors. For example, 15 = 3 x 5, 16 = 2 x 2 x 2 x 2, 18 = 3 x 3 x 2, etc. If, in the prime factorisation of 15, a 2 is multiplied to the prime factors, then, 3 x 5 x 2 = 30; which is another number, with a unique set of prime factors; 3, 5 and 2. Thus, on multiplication of 3 and 5, we can only get 15, making the prime factorisation unique. However, since the order in which numbers are multiplied doesn't matter, or 3 x 5 = 5 x 3 = 15; thus, the factorisation is unique, except for the order in which the prime factors occur.
Hope this information will clear your doubts about this topic.
If you have any more doubts, please ask here on the forum and our experts will help you out as soon as possible.
Regards