Question

Define fundamental theorem of arithmetic and

Euclid’s DivisionLemma.

Ques.2 Find the HCF using Euclid’s Division

Algorithm.(a)196 , 38220

(b) 240 , 6552

Ques3. Prove that:

(a)√ + √ is an irrational number.

(b) 5 + √ is an irrational number.

Ques4. Show that any odd positive integer is of the form

6q + 1 or6q + 3 or 6q + 5 for some integer q.

Ques5. Find the greatest number that will divide 1251, 9377 and

15628 leaving remainders 1, 2 and 3 respectively.

Ques 6. In a seminar the number of participants in Maths,

Physics and Biology are 336, 240 and 96. Find the minimum

number of rooms required if in each room the same number

of participants is to beseated and all of them of the same

subject.

Ques7. If HCF of 144 and 180 is expressed in the form 13m – 3,

find the valueof m.

Ques 8. Show that cannot end with the digit 0 or 5.

Ques 9. Prove that square of any positive integer is of the form 4m

or 4m + 1for some integer m.

Ques 10. Find the HCF and LCM of 288, 360 and 384 using Prime

Factorisation method.​

Answer 1

Answer:

HCF is 24 and LCM is 5760.

Step-by-step explanation:

Given numbers are 288 , 360 and 384.

To find: HCF & LCM by Prime factorization Method.

288 = 2 × 2 × 2 × 2 × 2 × 3 × 3.

360 = 2 × 2 × 2 × 3 × 3 × 5.

384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3