Question

4. The prime factorization forms of two numbers are 2¹ x 35 x 5³ x 7² a and 23 x 36 x 5 x 78.

a) Find the HCF of these two numbers in prime factorization form

b) Find the LCM of these two numbers in prime factorization form

please help me ;)

Answer 1

`\bold{\sf{\boxed{\huge{\blue{\underline{Solution 1}}}}}}`

`\sf{ we\:have\:to\:find\:the\:HCF\:of\:the \:two\:given \:numbers}`

`\bold{\underline{ Let's\: begin }}`

`\sf{2¹ × 35 × 5³ × 7² ...(1) }`

`\sf{23 × 36 × 5 × 78. ...(2)}`

`\bold{\underline{ write\: ( 1) \:and\: (2) \: simultaneously }}`

`\sf{ 2 × 5 × 7 ×5 × 5 × 5 × 7 × 7}`

`\sf{ 23 × 6 × 6 × 5 × 2 * 13 * 3 }`

`\bold{Thus, \:we\: got\: two\: common \:factor\: that\: is \:2 \:and \:5 }`

`\sf{\underline{Therefore}}`

`\sf{ 2 * 5 = 10}`

`\bold{\pink{Hence \:,\: HCF \:of\:the\: given\: number \:is \:10}}`

`\bold{\boxed{\huge{\blue{\underline{Solution 2}}}}}`

`\sf{ we\:have\:to\:find\:the\:LCM\:of\:the \:two\:given \:numbers}`

`\bold{\underline{ Let's\: begin }}`

`\sf{2¹ × 35 × 5³ × 7² ...(1) }`

`\sf{23 × 36 × 5 × 78. ...(2)}`

`\bold{\underline{ write\: ( 1) \:and\: (2) \: simultaneously }}`

`\sf{ 2 × 5 × 7 ×5 × 5 × 5 × 7 × 7}`

`\sf{ 23 × 6 × 6 × 5 × 2 × 13 × 3 }`

`\bold{Thus, \:we\: got\: two\: common \:factor\: that\: is \:2 \:and \:5 }`

`\sf{\underline{Therefore}}`

`\sf{ 2 × 5 × 7 × 5 × 5 × 5 × 7 × 7 × 23 × 6 × 6 × 13 × 3 }`

`\bold{\pink{Hence \:,\: LCM \:of\:the\: given\: number \: = 9230130000}}`