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Find all the prime factors of 1729 and arrange them in ascending order. Also, state the relation, if any, between two constructive prime factors.
Prime factorization is a way of expressing a number as a product of its prime factors.
Answer: The prime factors of 1729 arranged in ascending order are 7 < 13 < 19.
Let's find all the prime factors of 1729.
To find the prime factors of 1729, we will prime factorize 1729 as shown below.
1729 = 7 × 13 × 19
Factors of 1729 arranged in ascending order will be 7 < 13 < 19
Let's find the difference between these prime factors.
19 - 13 = 6, 13 - 7 = 6
Hence, we observe that the difference between the consecutive prime numbers is constant which is 6.
Therefore, the prime factors of 1729 arranged in ascending order is 7 < 13 < 19, and the relationship between any two consecutive prime factors is that they have a common difference of 6 between them.