Question

1. Answer the following question:
a) check whether 6 to the power n can end with the digit 0 for any natural number n.
b) explain why 7 * 11 *13 + 13 and 7 *6 *5 * 4 *3 * 2 * 1 + 5 are composite number.
c) find the LCM and HCF of the following pair of integer and verify that LCM * HCF equal to the product of the two number.
(i) 25 and 209
(ii) 234 and 545
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Answer 1

Answer:

I have mentioned the answer in the pic...

hope it helps..

Answer 2

Answer:

a) ans =》no , it cannot end with 0

b) ans =》yes they are composite number

c) ans=》(i) HCF = 1 and LCM = 5225

(ii) HCF = 1 and LCM = 127530

Step-by-step explanation:

a) ans=》since 6 dose not have both "2" and "5" in it's factor it cannot end with 0

b) ans=》7×11×13+13 = 1014

since 1014 is an even number it can be divided by 2 and it means it's composite number

7×6×5×4×3×2×1+5 = 99,646

since 99,646 is is an even number it can be divided by 2 it means it's composite number

c) ans=》(i) 25 = 5 × 5

209 = 11×19

HCF = 1 (since they are co-prime numbers)

LCM = 5 × 5 × 11 × 19 = 5225

also 25 × 209 = 5225 and 1 × 5225 = 5225

(ii) 234 = 2 × 3³ × 13

545 = 5 × 109

HCF = 1 (since they are co-prime numbers)

LCM = 2 × 3³ × 5 × 13 × 109 = 99,646

also 234 × 545 = 99,646 and 1 × 99,646 = 99,646

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