Divisibility Rule of 465

The divisibility rule for 465 is a method by which we can determine if a number is divisible by 465 without using the division method. Check whether 930 is divisible by 465 with the divisibility rule.

Step 1: Check if the number is divisible by 5. Since 930 ends in 0, it is divisible by 5.

Step 2: Check if the number is divisible by 3. Add the digits: 9+3+0=12. Since 12 is divisible by 3, 930 is also divisible by 3.

Step 3: Check if the number is divisible by 31 (since 465=5×3×31 and we have already checked for 5 and 3). Divide 930 by 31: 930÷31=30, which is an integer.

Since 930 is divisible by 5, 3, and 31, it is divisible by 465.

Knowing the individual divisibility rules for 5, 3, and 31 will help you master the divisibility rule for 465. Let’s learn a few tips and tricks for this rule.

• Know the multiples of 465: Memorize the multiples of 465 (465, 930, 1395, etc.) to quickly check divisibility.

• Use the properties of factors: If a number is divisible by all its prime factors (5, 3, and 31 for 465), then it is divisible by 465.

• Repeat the process for large numbers: For larger numbers, ensure divisibility by each factor before concluding. For example, check if 1860 is divisible by 465. Since 1860 ends in 0, it is divisible by 5.
  
  The sum of the digits, 1+8+6+0=15, is divisible by 3. Dividing 1860 by 31 gives an integer (60), thus confirming divisibility by 31. Therefore, 1860 is divisible by 465.

• Use the division method to verify: Cross-check your results using the division method to verify and solidify your understanding.

• Divisibility Rule: A set of guidelines to determine if a number is divisible by another without division.

• Multiples: Numbers obtained by multiplying a given number by integers. For example, multiples of 465 are 465, 930, 1395, etc.

• Factors: Numbers that divide another number exactly without leaving a remainder. For 465, the factors are 5, 3, and 31.

• Integer: Whole numbers, including negatives and zero.

• Verification: The process of confirming accuracy, such as using division to check results.