Question

4. Given that HCF (306, 657)=9, find LCM (306, 657). 5. Check whether 6" can end with the digit 0 for any natural number n. 6. Explain why 7x 11 x 13 + 13 and 7 x6x5 x 4 x 3 x 2x1 + 5 are composite numbers. ​

Answer 1

Answer:

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Answer 2

Answer:

4.) LCM=22134

5.) No

6.) Proof given below

Step-by-step explanation:

4.) Since, Product of numbers = LCM×HCF

306×657=LCM×9

LCM=22134

5.) 6ⁿ = (2×3)ⁿ = 2ⁿ×3ⁿ

Hence, it does not have 5 in its prime factors for 2×5=10

Hence, it cannot end with the digit 0.

6.) (i) 7×11×13+13 = 13(7×11+1)            (by taking common)

Hence, it has 13 as a factor other than 1 and itself.

Hence, it is a composite number.

6.) (ii) 7×6×5×4×3×2×1+5 = 5(7×6×4×3×2×1+1)      (by taking common)

Hence, it has 5 as a factor other than 1 and itself.

Hence, it is a composite number.