Divisibility Rule For 35 With Examples

Divisibility Rule for 35

The divisibility rule for 35 is based on its prime factors, which are 5 and 7. A number is divisible by 35 if it meets the criteria for both of these factors. Here’s a detailed explanation of how to check for divisibility by 35, along with examples.

Divisibility Rules for 35

To determine if a number is divisible by 35, follow these steps:

1. Divisibility by 5:

• A number is divisible by 5 if its last digit is either 0 or 5.

1. Divisibility by 7:

• A number is divisible by 7 if, after performing a specific calculation, the result is divisible by 7. A common method is to double the last digit, subtract it from the rest of the number, and check if the result is divisible by 7.

Combined Rule

For a number to be divisible by 35, it must satisfy both conditions:

• It must be divisible by 5.
• It must be divisible by 7.

Examples

Example 1: Check if 105 is divisible by 35

1. Check for 5:

• Last digit: 5.
• Conclusion: 105 is divisible by 5.

1. Check for 7:

• Last digit: 5, double it: (5 x 2 = 10).
• Remaining number: (10 – 10 = 0).
• (0/7 = 0) (no remainder).
• Conclusion: 105 is divisible by 7.

Since 105 is divisible by both 5 and 7, it is divisible by 35.

Example 2: Check if 210 is divisible by 35

1. Check for 5:

• Last digit: 0.
• Conclusion: 210 is divisible by 5.

1. Check for 7:

• Last digit: 0, double it: (0 x 2 = 0).
• Remaining number: (21 – 0 = 21).
• (21/7 = 3) (no remainder).
• Conclusion: 210 is divisible by 7.

Since 210 is divisible by both 5 and 7, it is divisible by 35.

Example 3: Check if 155 is divisible by 35

1. Check for 5:

• Last digit: 5.
• Conclusion: 155 is divisible by 5.

1. Check for 7:

• Last digit: 5, double it: (5 x 2 = 10).
• Remaining number: (15 – 10 = 5).
• (5/7 ≈ 0.71) (not an integer).
• Conclusion: 155 is not divisible by 7.

Since 155 is not divisible by 7, it is not divisible by 35.

Example 4: Check if 420 is divisible by 35

1. Check for 5:

• Last digit: 0.
• Conclusion: 420 is divisible by 5.

1. Check for 7:

• Last digit: 0, double it: (0 x 2 = 0).
• Remaining number: (42 – 0 = 42).
• (42/7 = 6) (no remainder).
• Conclusion: 420 is divisible by 7.

Since 420 is divisible by both 5 and 7, it is divisible by 35.

Example 5: Check if 100 is divisible by 35

1. Check for 5:

• Last digit: 0.
• Conclusion: 100 is divisible by 5.

1. Check for 7:

• Last digit: 0, double it: (0 \times 2 = 0).
• Remaining number: (10 – 0 = 10).
• (10/7 ≈ 1.43) (not an integer).
• Conclusion: 100 is not divisible by 7.

Since 100 is not divisible by 7, it is not divisible by 35.

Summary

To determine if a number is divisible by 35:

1. Check if it is divisible by 5 (last digit is 0 or 5).
2. Check if it is divisible by 7 (using the doubling method or direct division).

If a number meets both criteria, it is divisible by 35. This method provides a quick and effective way to assess divisibility, especially with larger numbers.