"The product of three consecutive positive integers is divisible … - Vidyadip

Question

"The product of three consecutive positive integers is divisible by 6". Is this statement true or false"? Justify your answer.

✓

Answer

Yes, the given statement is true.
Three consecutive positive integers are n, (n + 1), (n + 2). Out of 3 consecutive integers, one will be even and other will be divisible by 3.
So, the product of all three becomes dividsible by 6,
e.g., 13, 14, 15 here 14 is even, 15 is divisible by 3.
So, 13 × 14 × 15 is divisible by 6.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Real Numbers→Real Numbers — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

If P(x, y) is a point equidistant from the points A(6, - 1) and B(2, 3), show that x - y = 3.

A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60 to the horizontal. Find the length of the string to the nearest metre.

What is the cumulative frequency of the modal class of the following distribution?

Class	3-6	6-9	9-12	12-15	15-18	18-21	21-24
Frequency	7	13	10	23	4	21	16

Find the mean of the following data:

$x$	$19$	$21$	$23$	$25$	$27$	$29$	$31$
$f$	$13$	$15$	$16$	$18$	$16$	$15$	$13$

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150m, find the distance between the objects.

Name the quadrilateral formed, if any, by the following points, and given reason for your answers:A(4, 5), B(7, 6), C(4, 3), D(1, 2).

Out of the two concentric circles, the radius of the outer circle is $5 \ cm$ and the chord $AC$ of length $8 \ cm$ is a tangent to the inner circle. Find the radius of the inner circle.

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

The $9^{\text {th }}$ term of an AP is -32 and The sum of its $11^{\text {th }}$ and $13^{\text {th }}$ terms is -94 . Find the common difference of the AP.

In a right triangle ABC, right angled at C, if $\angle\text{B} = 60^\circ$ and AB = 15 units. Find the remaining angles and sides.