Divisibility Rule of 154

The divisibility rule for 154 is a method to determine if a number is divisible by 154 without performing division. Let’s check whether 308 is divisible by 154 using the divisibility rule.

Step 1: Check divisibility by 2. The number 308 ends in 8, which is even, so it is divisible by 2.

Step 2: Check divisibility by 7. Apply the divisibility rule for 7: multiply the last digit (8) by 2, resulting in 16. Subtract this from the remaining leading part (30), giving 30 - 16 = 14. Since 14 is a multiple of 7, 308 is divisible by 7.

Step 3: Check divisibility by 11. For 11, alternate summing the digits: (3 + 8) - 0 = 11, which is a multiple of 11.

Step 4: Since 308 is divisible by 2, 7, and 11, it is also divisible by 154 (as 154 = 2 × 7 × 11).

• Memorize the prime factors: Know that 154 is the product of 2, 7, and 11. If a number is divisible by these three primes, it is divisible by 154.
   
• Use smaller tests: First, check divisibility by 2, then 7, and finally 11, to quickly determine if a number is divisible by 154.
   
• Break down large numbers: For large numbers, apply the prime factor tests separately and sequentially to simplify the calculation.
   
• Verify with division: Use actual division to confirm results when in doubt or to reinforce understanding of divisibility.
   

• Divisibility rule: A set of guidelines to determine if one number is divisible by another without performing division.
   
• Prime factors: Basic numbers (greater than 1) that multiply together to give a number, such as 2, 7, and 11 for 154.
   
• Multiple: A number that can be divided by another number without a remainder. For example, 308 is a multiple of 154.
   
• Integer: Whole numbers, including negative numbers, positive numbers, and zero.
   
• Subtraction: The operation of finding the difference between numbers, used in checking divisibility by 7.