What is the number of the ordered triplets ABC such that ABC 108?

The numbers (a, b, c) can be 3,4,9 or 2,6,9 or 2,3,18….. and so on. For each set there will be 3! Possibilities. Therefore, if number of sets is n, the total number of ordered triplets are n x 3!…

How many triples of non negative integers abc satisfy ABC s and ABC T code?

So, in total there are 11 ordered triples satisfying the given conditions (0

How do you find how many positive divisors a number has?

In general, if you have the prime factorization of the number n, then to calculate how many divisors it has, you take all the exponents in the factorization, add 1 to each, and then multiply these “exponents + 1″s together.

What is the number of ordered triples?

An ordered triple is a list of 3 elements written in a certain order. As with ordered pairs, order is important. For example, the numbers 1, 2 and 3 can form 6 ordered triples: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1).

Is 2 a positive integer?

Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5, .

How many positive integer divisors does 144 have?

The number 144 can be divided by 15 positive divisors (out of which 12 are even, and 3 are odd). The sum of these divisors (counting 144) is 403, the average is 26.,866.

What is an ordered triple in math?

In general, a solution of a system in three variables is an ordered triple (x, y, z) that makes ALL THREE equations true. In other words, it is what they all three have in common. So if an ordered triple is a solution to one equation, but not another, then it is NOT a solution to the system.

What is the total count of triplets that satisfy the given property?

Explanation: All possible triplets that satisfy the given property are (1, 1, 1) and (2, 2, 2). Therefore, the total count is 2. Recommended: Please try your approach on {IDE} first, before moving on to the solution.

How many triplets are there that are multiples of K?

Given two positive integers N and K, the task is to count the number of triplets (a, b, c) such that 0 < a, b, c < N and (a + b), (b + c) and (c + a) are all multiples of K. Explanation: All possible triplets that satisfy the given property are (1, 1, 1) and (2, 2, 2). Therefore, the total count is 2.

Is (a + B) – (C + B)(A – C) a multiple of K?

As (a + b) is a multiple of K and (c + b) is a multiple of K. Therefore, (a + b) − (c + b) = a – c is also a multiple of K, i.e., a ≡ b ≡ c (mod K). From the above observations, the result can be calculated for the following two cases: