Question

Sum of three consecutive even numbers is equal to the product of first four prime numbers

Answer 1

$\huge\mathfrak{Solution:-}$

First 4 prime numbers are 2,3,5,7

Product=210

Let three consecutive even numbers be 2x,2x+2,2x+4

$\mathtt 2x+2x+2+2x+4=210\\</p><p>6x+6=210\\</p><p>6x=204\\</p><p>x=34$

Numbers are 68,70,72

Answer 2

The three numbers are 68, 70, and 72.

Given:

The sum of the three consecutive even integers is equal to the product of the first four prime numbers.

To Find:

The three even numbers.

Solution:

Even numbers are those that are multiples of 2

Let us assume that the first even number is 2x.

Hence the three consecutive numbers will be 2x, 2x + 2, 2x + 4.

Prime numbers are those that have only two factors, 1 and the number itself.

Now, the first four prime numbers are 2, 3, 5, and 7.

The product of first four prime numbers = 2 x 3 x 5 x 7 = 210

Now, we are given that the sum of the three consecutive even integers is equal to the product of the first four prime numbers.

2x + ( 2x + 2) +( 2x + 4) = 210

6x + 6 = 210

6x = 204

x = 34.

So the three numbers are

2x = 2(34) = 68.

2x + 2 = 2(34) + 34 = 70.

2x +4 =  2(34) + 4 = 70.

Hence, the three numbers are 68, 70, and 72.

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