Question

The sum of two numbers is 45 and their product is 500. the g.c.f. of the numbers is

Answer 1

Answer:

Step-by-step explanation:

Here is the solution to find HCF Of two numbers

Answer 2

The G.C.F. of numbers is 5.

Numbers are 20 and 25.

Given:

• The sum of two numbers is 45
• and their product is 500.

To find:

• Find the g.c.f. of the numbers.

Solution:

Concept to be used:

• Assume the numbers as variables.
• Form equations and solve.

Step 1:

Form the equations.

Let the numbers are x and y.

So,

$\bf x + y = 45...eq1$

and

$\bf xy = 500...eq2$

Step 2:

Put value of y from eq1 in eq2

$x(45 - x) = 500$

or

$- {x}^{2} + 45x - 500 = 0$

or

$\bf {x}^{2} - 45x + 500 = 0$

Step 3:

Solve quadratic equation to find Value of x.

${x}^{2} - 20x - 25x + 500 = 0$

or

$x(x - 20) - 25(x - 20) = 0$

or

$(x - 20)(x - 25) = 0$

or

$\bf x = 20 \: or \: 25$

Step 4:

Taking x= 20

$20 + y = 45$

or

$y = 45 - 20$

or

$\bf y = 25$

Thus,

The numbers are 20 and 25 or vice versa.

Step 5:

Find prime factors of numbers.

$20 = 2 \times 2 \times 5$

and

$25 = 5 \times 5$

Thus,

Greatest common factor of 20 and 25 is 5.

Learn more:

1) Find the greatest number that divides 79115 and 163, leaving remainder 7 in each case

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