Question

Find the HCF of 75 ,100 and 140 numbers by long division method

Answer 1

Answer:

5 is the required HCF of 75, 100, and 140.

Step-by-step explanation:

Explanation:

Given that, 75, 100, and 140.

• HCF - The greatest number that divides each of the two or more numbers is known as the HCF, or the highest common factor.

• The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD)

• Example - let two numbers 24 and 36. Common factor of 24 and 36 are 2 , 2, 3 .So, the hcf of 24 and 36 is 12 (2× 2 ×3).

Step 1:

We have, 75, 100 and 140

By long division method,

On dividing 100 by 75

           75) 100( 1

                  7 5

                -            

                  25) 75  ( 3

                         75

                      -          

                        x x

⇒100 = 75 × 1 + 25

   75 = 25 × 3 + 0

Here we can see that on  diving 75 by 25 the remainder become zero.

Now, we divide 140 by 25,

              25  ) 140    (5

                       125

                      -          

                        1 5) 25 (1

                                15

                             -          

                                10 )  15  (

                                          10

                                     -                

                                           5 ) 10 ( 2

                                                  10

                                               -        

                                              xxx

On dividing 10  with 5 the remainder become zeroes.

Therefore, HCF of 75 , 100 and 140 = 5

Final answer:

Hence, 5 is the required HCF of 75, 100, and 140.

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Answer 2

Given expressions are 75, 100, and 140

To find: We need to find the HCF by using the long division method.

$\ \ \ \ \ \ \ 1\\75 \kern.25em\smash{\raise.3ex\hbox{ \big) }} \mkern-8mu \overline{\enspace\strut#100} }\begin{document}$

       $\underline{75}\\25$

$\ \ \ \ \ \ 3\\25 \kern.25em\smash{\raise.3ex\hbox{ \big) }} \mkern-8mu \overline{\enspace\strut#75} }\begin{document}$

     $75\\\overline{\ 0\ }$

HCF of 75 and 100 is 25.

       $5$

$25 \kern.25em\smash{\raise.3ex\hbox{ \big) }} \mkern-8mu \overline{\enspace\strut#140} }\begin{document}\ \ \ \ \ \Mydiv{125}\end{document}$    $1$

     $\overline{\ 15\ } \kern.25em\smash{\raise.3ex\hbox{ \big) }} \mkern-8mu \overline{\enspace\strut#25} }\begin{document}\ \ \ \ \ \ \ \Mydiv{15}\end{document}$    $1$

            $\overline{\ 10\ } \kern.25em\smash{\raise.3ex\hbox{ \big) }} \mkern-8mu \overline{\enspace\strut#15} }\begin{document}\ \ \ \ \ \ \ \Mydiv{10}\end{document}$   $2$

                    $\overline{\ 5\ } \kern.25em\smash{\raise.3ex\hbox{ \big) }} \mkern-8mu \overline{\enspace\strut#10} }\begin{document}\ \ \ \ \ \ \Mydiv{10}\end{document}$

                           $\overline{\ 0\ }$

The HCF of the expressions 75, 100, and 140 is 5.

To learn more about HCF from the given link

https://brainly.in/question/3098913

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