Why the product of three consecutive numbers is always divisible by 6?

Why the product of three consecutive numbers is always divisible by 6?

Now, we have shown that out of the three consecutive numbers, one of them is always divisible by 2 and 3. Product of the three numbers is 13×14×15=2730. Now, 2730÷6=455. Hence, the product of the given triplet is divisible by 6.

How do you prove three consecutive integers is divisible by 6?

n3 − n = (n − 1)n(n + 1) is the product of three consecutive integers and so is divisible by 6.

Is integer divisible by 6?

A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156. [We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2]. 42 is divisible by 2.

Why is the product of three consecutive numbers divisible by three?

Let three consecutive positive integers are (n, n + 1, n + 2) where n is any positive real number. So we can say that one of the numbers among (n, n + 1 and n + 2) is always divisible by 3. Therefore the product of numbers n(n+1)(n+2) is always divisible by 3.

Is it true that product of 3 consecutive natural numbers is always divisible by 6 Justify?

Thus, n(n+1)(n+2) is divisble by 6. …

Is it true that product of 3 consecutive?

Hence, (III) is not true. Thus, the answer is D. Product of n consecutive integers is always divisible by n!

What is the product of three consecutive positive integers?

Answer Expert Verified Let n (n +1) and (n + 2) are three consecutive positive integers. Then their product is n (n +1)(n+2). Since any positive integer is of the form 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4, 6q + 5. n (n + 1) (n + 2) = 12 (3q + 1) (2q + 1) (3q + 2), Which is divisible by 6.

When you multiply a number by 3 the product is divisible by 6?

Therefore as we are multiplying the numbers together, multiplying a multiple of 3 and a multiple of 2 gives us a multiple of 6. Hence the product will be divisible by 6.

Is the product of three consecutive positive integers is divisible by 6?

Prove that the product of three consecutive positive integers is divisible by 6. so, we can say that one of the numbers n, n + 1 and n + 2 is always divisible by 3. n (n + 1) (n + 2) is divisible by 3.

What is the common form of integers divisible by 3?

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. Some examples of numbers divisible by 3 are as follows. The number 85203 is divisible by 3 because the sum of its digits 8+5+2+0+3=18 is divisible by 3.

When a number is divided by 7 its remainder is 4?

square of 12 = 144. hence it is proved that by dividing the square of that no. by 7, we get 4 as remainder. Hope it helped!

What is the largest possible remainder when a number is divided by 7?

6

When a number is divided by 12 the quotient is 15 and the remainder is 6 What is the number?

Answer. Answer: The number is 190.

What is the remainder when 323232 is divided by 7?

41 divided by 7 gives the remainder as 4.