What is the divisibility rule for 2?

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). For example, 124 is divisible by 2 because 4 is even.

How can you determine if a number is divisible by 3?

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, for the number 123, the sum is 1 + 2 + 3 = 6, which is divisible by 3.

If a number n leaves a remainder of 4 when divided by 7, what can you say about n?

This means that n can be expressed in the form n = 7k + 4, where k is an integer. For example, if k = 2, then n = 7*2 + 4 = 18, which gives a remainder of 4 when divided by 7.

Determine the remainder when 145 is divided by 6.

To find the remainder, perform the division: 145 ÷ 6 = 24 R1. Thus, the remainder is 1.

Is 108 divisible by 4? Explain your reasoning.

Yes, a number is divisible by 4 if the number formed by its last two digits is divisible by 4. The last two digits of 108 are 08, and since 08 ÷ 4 = 2, 108 is divisible by 4.

What is the divisibility rule for 5?

A number is divisible by 5 if its last digit is 0 or 5. For example, 135 is divisible by 5 because it ends with 5.

How can you determine if a number is divisible by 9?

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, for the number 234, the sum is 2 + 3 + 4 = 9, which is divisible by 9.

If a number n gives a remainder of 3 when divided by 5, which of the following could be n? (A) 8 (B) 13 (C) 18 (D) 23

The answer is (B) 13. When 13 is divided by 5, it gives a remainder of 3 (13 ÷ 5 = 2 R3).

Find the remainder when 250 is divided by 7.

To find the remainder, perform the division: 250 ÷ 7 = 35 R3. Thus, the remainder is 3.

Is 256 divisible by 8? Explain your reasoning.

Yes, a number is divisible by 8 if the number formed by its last three digits is divisible by 8. The last three digits of 256 are 256, and since 256 ÷ 8 = 32, 256 is divisible by 8.

What is the rule for divisibility by 11?

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or divisible by 11. For example, for 2728, (2 + 2) - (7 + 8) = 4 - 15 = -11, which is divisible by 11.

If a number n has a remainder of 2 when divided by 4, what can you say about n?

This means that n can be expressed as n = 4k + 2, where k is an integer. For example, if k = 3, then n = 4*3 + 2 = 14, which gives a remainder of 2 when divided by 4.

What is the relationship between divisibility and prime factorization?

A number is divisible by another if all prime factors of the second number are present in the first number's prime factorization with at least the same multiplicity. For example, 12 (2² * 3) is divisible by 4 (2²) but not by 6 (2 * 3) if we consider 18 (2 * 3²).

Find the remainder when 123456 is divided by 9.

To find the remainder, calculate the sum of the digits: 1 + 2 + 3 + 4 + 5 + 6 = 21. Since 21 ÷ 9 = 2 R3, the remainder is 3.

If a number is divisible by both 2 and 3, is it also divisible by 6? Explain.

Yes, if a number is divisible by both 2 and 3, it is also divisible by 6 because 6 is the least common multiple (LCM) of 2 and 3.