Question

1. Write prime Factors of 27300.
2. Given that HCF ( 2520, 6600)= 40 and LCM (2520,6600) = 252×K, FIND K
3. Find HCF OF 4284 AND 6762. FIND LCM ALSO.
4. HCF AND LCM OF E36 AND 54 BY PRIME FACTORISATION METHOD.
5. FIND HCF & LCM of 105 and 1515 PRIME FACTORISATION METHOD
6. SHOW THAT 17 × 41× 43 × 61 + 43 IS A COMPOSITE NUMBER.
7. SHOW THAT ANY POSITIVE ODD INTEGER IS OF THE FORM 8q+ 1, 8q+ 5 , 8q + 7 where q is some integer

QUESTIONS FOR BRILLIANT STUDENTS

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Answer 1

$\sf{\underline{Question\:No.\:1}}$

$\sf{Prime\:Factors:}$

$\boxed{\sf{27300 = 2 \times 2 \times 3 \times 5 \times 5 \times 7 \times 13}}$

$\sf{\underline{Question\:No.\:4}}$

$\boxed{\sf{336 = 2 \times 2 \times 2 \times 2 \times 3 \times 7}}$

$\boxed{\sf{54 = 2 \times 3 \times 3 \times 3}}$

$\sf{So:}$

HCF (336,54) = 6

LCM (336,54) = $2^{4}$ × $3^{3}$ × $7$ = 3024

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$\sf{\underline{NOTE:}}$ For question no. 2, 3, 5, 6 and 7, check these attachments.