This page explains the divisibility rules for whole numbers from 2 to 10. Each rule is presented with examples, followed by practice questions and complete solutions.
A whole number \( n \) is said to be divisible by another whole number \( m \) if the division \[ \frac{n}{m} \] results in a remainder of \(0\). In this case, \( m \) is called a factor of \( n \).
Example: \[ \frac{15}{5} = 3 \] Since the remainder is \(0\), the number \(15\) is divisible by \(5\). This can also be written as: \[ 15 = 3 \times 5 \] Both \(3\) and \(5\) are factors of \(15\). Similarly, \[ \frac{15}{3} = 5 \] so \(15\) is also divisible by \(3\).
Given a whole number, the following tests help determine whether it is divisible by another number such as \(2, 3, 4, \dots, 10\).
A whole number is divisible by \(2\) if its last digit is \(0, 2, 4, 6,\) or \(8\).
Example: The number \(23464568\) is divisible by \(2\) because its last digit is \(8\).
A whole number is divisible by \(3\) if the sum of its digits is divisible by \(3\).
Example: \[ 1 + 2 + 7 + 2 = 12 \] Since \(12\) is divisible by \(3\), the number \(1272\) is divisible by \(3\).
A whole number is divisible by \(4\) if the number formed by its last two digits is divisible by \(4\).
Example: The last two digits of \(1869520\) are \(20\), and since \[ \frac{20}{4} = 5 \] the number \(1869520\) is divisible by \(4\).
A whole number is divisible by \(5\) if its last digit is \(0\) or \(5\).
Example: The number \(52745\) is divisible by \(5\) because its last digit is \(5\).
A whole number is divisible by \(6\) if it is divisible by both \(2\) and \(3\).
Example: The number \(1890\) is divisible by \(2\) (last digit \(0\)) and divisible by \(3\) since \[ 1 + 8 + 9 + 0 = 18 \] Therefore, \(1890\) is divisible by \(6\).
A whole number is divisible by \(8\) if the number formed by its last three digits is divisible by \(8\).
Example: The last three digits of \(18567160\) are \(160\), and \[ \frac{160}{8} = 20 \] So the number \(18567160\) is divisible by \(8\).
A whole number is divisible by \(9\) if the sum of its digits is divisible by \(9\).
Example: \[ 1 + 0 + 0 + 6 + 5 + 0 + 6 = 18 \] Since \(18\) is divisible by \(9\), the number \(1006506\) is divisible by \(9\).
A whole number is divisible by \(10\) if its last digit is \(0\).
Example: The number \(12635360\) is divisible by \(10\) because its last digit is \(0\).
\(4,\; 5,\; 100,\; 408,\; 777,\; 52340,\; 8879\)
\(33,\; 53,\; 105,\; 5554,\; 777,\; 9222321\)
\(100,\; 3005,\; 12940,\; 5554,\; 7777,\; 9222352\)
\(60,\; 362,\; 12940,\; 50016505\)
\(120,\; 648,\; 12941,\; 309948\)
\(160,\; 11048,\; 12941,\; 10056720\)
\(109,\; 10233,\; 12941,\; 1946700\)
\(100,\; 3005,\; 12940\)
Divisible by 2: \(4,\; 100,\; 408,\; 52340\)
Divisible by 3: \(33,\; 105,\; 777,\; 9222321\)
Divisible by 4: \(100,\; 12940,\; 9222352\)
Divisible by 5: \(60,\; 12940,\; 50016505\)
Divisible by 6: \(120,\; 648,\; 309948\)
Divisible by 8: \(160,\; 11048,\; 10056720\)
Divisible by 9: \(10233,\; 1946700\)
Divisible by 10: \(100,\; 12940\)