Divisibility Rule of 705

The divisibility rule for 705 is a method to check if a number is divisible by 705 without performing division. Let's check whether 352,755 is divisible by 705 using the divisibility rule.

Step 1: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. Here, 352,755 ends in 5, so it is divisible by 5.

Step 2: Check divisibility by 3. Add all digits of the number: 3+5+2+7+5+5=27. Since 27 is divisible by 3, 352,755 is divisible by 3.

Step 3: Check divisibility by 47. Divide the number by 47 and see if the remainder is 0. Here, 352,755 ÷ 47 = 7,505 with no remainder, confirming divisibility by 47.

Since 352,755 is divisible by 5, 3, and 47, it is divisible by 705 (5×3×47).

Learning divisibility rules will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 705.

Know the prime factors:

Memorize the prime factors of 705 (5, 3, 47) to quickly check divisibility.

Use the division method for confirmation:

After using divisibility rules, you can use division to verify your results.

Repeat the process for large numbers:

If dealing with large numbers, break down the process by checking divisibility by 5, 3, and 47 separately.

Simplify calculations:

When checking for divisibility by 3, always simplify your sum of digits by comparing it with known multiples of 3.

Practice regularly:

Regular practice will help avoid confusion and make the process second nature.

• Divisibility Rule: A method to determine if a number can be divided by another number without a remainder.

• Prime Factors: The prime numbers that multiply together to yield the original number, such as 5, 3, and 47 for 705.

• Remainder: The amount left after division when a number does not divide evenly.

• Integer: A whole number that can be positive, negative, or zero.

• Verification: The process of checking calculations to ensure accuracy, often using division to confirm results.