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Q.

State true or false:
The prime factorization of a positive integer 45470971 is $7^{2} \times 2^{2} \times 17^{3} \times 11$ .

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a

True

b

False

answer is B.

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Detailed Solution

The given number is 45470971.
The prime factorisation of

45470971 = 7 \times 7 \times 13 \times 13 \times 17 \times 17 \times 19

\Rightarrow 45470971 = 7^{2} \times 13^{2} \times 17^{2} \times 19

Therefore, the given statement is false.
The correct statement would be that the prime factorisation of 45470971 is

7^{2} \times 13^{2} \times 17^{2} \times 19

.
Hence, option 2 is correct.

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State true or false:The prime factorization of a positive integer 45470971 is 72×22×173×11.