Question

Using all three methods ,find HCF. of 20 , 25, and 50 . Methods common, prime factorisation, division.​

Answer 1

✮ Question -:

Using all three methods (methods common, prime factorisation, division) find HCF. of 20 , 25, and 50 .

✮ Explanation -:

We can find the HCF of any number using three methods -

• Common Factor
• Prime Factorisation
• Division

Common Factor :

Step 1

• Find all the factors of the given no.

Step 2

• Find the common factor

Step 3

• Take the highest factor from the common factor

$\small\sf{ 20 = \boxed{1}, 2, 4, \boxed{5}, 10 \: and \: 20.}$

$\small\sf{ 25 = \boxed{1}, \boxed{5} \: and \: 25.}$

$\small\sf 50 = \boxed{1}, 2, \boxed{5}, 10, 25 \: and \: 50.$

Here 5 is the highest factor

HCF of 20, 25 and 50 is 5.

Prime Factorisation :

Step 1

• Find the prime factor of the given number by division method.

Step 2

• Find out the common prime factor

Step 3

• The product of the common prime factor gives the HCF of the number

$\small\sf{ Prime \: Factorisation \: of \: 20 = 2 × 2 × \boxed{5}}$

$\small\sf{ Prime \: Factorisation \: of \: 25 = 5 × \boxed{5}}$

$\small\sf{ Prime \: Factorisation \: of \: 50 = 2 × 5 × \boxed5}$

The prime factor common to the numbers is 5

HCF = 5

Division method :

Step 1

• First find the HCF of any two numbers, from that two numbers divide the greater number with the smaller number then divide the remainder with the smaller number continue in the same way till no remainder left.

Step 2

• Find the HCF of the third number and the HCF of first two numbers.

Refer to the attachment for solution.

$\rule{182pt}{3pt}$