Which statement is true about the divisibility rules for number 6?

Rule for 6: If a number is divisible by 2 and 3 the number is divisible by 6. This means 6 will divide any even number whose digits sum to a multiple of 3.

How do you know something is divisible by 5?

A number is divisible by 5 if the number’s last digit is either 0 or 5. Divisibility by 5 – examples: The numbers 105, 275, 315, 420, 945, 760 can be divided by 5 evenly. The numbers 151, 246, 879, 1404 are not evenly divisible by 5.

What is the mathematical expression of the sum of three consecutive even integers?

Explanation: Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108.

How do you know if a number is divisible by another number?

A number is divisible by another number if it can be divided equally by that number; that is, if it yields a whole number when divided by that number. For example, 6 is divisible by 3 (we say “3 divides 6”) because 6/3 = 2, and 2 is a whole number.

How do you know if something is divisible by 5?

Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5. If the last digit in the number is 0, then the result will be the remaining digits multiplied by 2.

What is the next step in mathematical induction?

The next step in mathematical induction is to go to the next element after k and show that to be true, too: If you can do that, you have used mathematical induction to prove that the property P is true for any element, and therefore every element, in the infinite set.

Is 6 N – 1 always divisible by 5?

Prove 6 n − 1 is always divisible by 5 for n ≥ 1. Base Case: n = 1: 6 1 − 1 = 5, which is divisible by 5 so TRUE. Assume true for n = k, where k ≥ 1 : 6 k − 1 = 5 P.

How do you prove a property by induction?

Proof by Induction. Your next job is to prove, mathematically, that the tested property P is true for any element in the set — we’ll call that random element k — no matter where it appears in the set of elements. This is the induction step. Instead of your neighbors on either side, you will go to someone down the block, randomly,…

What is the remainder of 6K after division by 5?

We can show by induction that 6 k has remainder 1 after division by 5. The base case k = 1 (or k = 0) is straightforward, since 6 = 5 ⋅ 1 + 1. Now suppose that 6 k has remainder 1 after division by 5 for k ≥ 1. Thus 6 k = 5 ⋅ m + 1 for some m ∈ N. We can then see that = 5 ( 5 ⋅ m + m + 1) + 1. Thus 6 k + 1 has remainder 1 after division by 5.