Discussion

Explanation:

We first need to find all factors of (1890) × (130) × (170) and then remove those factors which are divisible by 45.

(1890) × (130) × (170) = (2 × 33 × 5 × 7) × (13 × 2 × 5) × (17 × 2 × 5)

⇒ 1890 × 130 × 170 = 23 × 33 × 53 × 7 × 13 × 17

∴ Total factors = (3 + 1)(3 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1) = 512

Now for factors that are divisible by 45, least power of 3 should be 2 and that of 5 should be 1. Powers of 2, 7, 13 and 17 can be anything.

∴ Total factors which are divisible by 45 = 4 × 2 × 3 × 2 × 2 × 2 = 192

⇒ Number of factors which are not divisible by 45 = 512 - 192 = 320.

Hence, 320.

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Doubts


Jainith said (2023-04-18 09:37:28)

pls elaborate the answer

Reply from Admin:

solution updated.


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