Question

The integer 6 is the product of two consecutive integers (6 = 2 × 3) and the product of three consecutive integers (6 = 1 × 2 × 3). What is the next integer greater than 6 that is both the product of two consecutive integers and the product of three consecutive integers? A.153 B.210 C.272 D.336 E.600

Answer 1

Answer:

B. 210

Step-by-step explanation:

Given:

$6=2\times3$

$6=1\times2\times3$

We need to find the next integer greater than 6 and is both the product of two consecutive integers and the product of three consecutive integers.

Solution:

From the given option we will find the factors of each.

a. 153

Now we will find the factors of 153.

Factors of 153 = $1, 3, 9, 17, 51, 153.$

From above we can see that 153 doesn't have factors which are consecutive integers

Hence from Above we can say that 153 is not the number which is the product of two consecutive integers and the product of three consecutive integers.

b. 210

Now we will find the factors of 210.

Factors of 210 = $1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210,$

So we can say that;

$210 =5\times6\times7$

Also;

$210 =14\times15$

From above we can see that;

210 is the number which is the product of two consecutive integers and the product of three consecutive integers.