1.

How many factors of the number 26 × 38 × 54 × 106 are multiple of 240?1). 5402). 6603). 5944). 792

Answer»

The prime factorization of 26 × 38 × 54 × 106 is 212 × 38 × 510.

240 can be prime-factorized as 24 × 3 × 5.

All factors of 212 × 38 × 510 that can be written as multiples of 240 will be of the form 24 × 3 × 5 × K.

212 × 38 × 510 = 24 × 3 × 5 × K 

⇒ K = 28 × 37 × 59.

The number of factors of N that are multiples of 240 is identical to the number of factors of K.

Number of factors of K = (8 + 1) (7 + 1) (9 + 1) = 9 × 8 × 10 = 720



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