what is 35 divisible by

Guri Bee

2 min read

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20-10-2024

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Is 35 Divisible By...? Exploring Divisibility Rules

The number 35 is a familiar one, but have you ever stopped to think about what numbers it is divisible by? Understanding divisibility rules can help you quickly determine factors without resorting to long division.

Let's break down the divisibility rules and see if 35 fits the bill:

1. Divisibility by 2:

• Rule: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
• 35: The last digit of 35 is 5, which is odd. Therefore, 35 is not divisible by 2.

2. Divisibility by 3:

• Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
• 35: The sum of the digits of 35 (3 + 5 = 8) is not divisible by 3. Therefore, 35 is not divisible by 3.

3. Divisibility by 5:

• Rule: A number is divisible by 5 if its last digit is either 0 or 5.
• 35: The last digit of 35 is 5. Therefore, 35 is divisible by 5.

4. Divisibility by 7:

• Rule: A number is divisible by 7 if twice the last digit, subtracted from the remaining part of the number, is divisible by 7.
• 35: Twice the last digit (5 x 2 = 10) subtracted from the remaining part (3) gives us -7, which is divisible by 7. Therefore, 35 is divisible by 7.

5. Divisibility by 10:

• Rule: A number is divisible by 10 if its last digit is 0.
• 35: The last digit of 35 is 5, not 0. Therefore, 35 is not divisible by 10.

In summary:

35 is divisible by 5 and 7. It's not divisible by 2, 3, or 10.

Additional Insights:

• It's helpful to remember that a number is divisible by its factors. Since 35 is divisible by 5 and 7, it's also divisible by their product, 35 (1 x 35 = 35).
• The divisibility rules can be used to quickly identify potential factors of larger numbers, making factorization easier.

Further Exploration:

• You can find additional divisibility rules for numbers like 4, 8, 9, and 11 on websites like Khan Academy or Purplemath.
• Explore the concept of prime factorization, which can help you break down any number into its prime factors.

By understanding these divisibility rules, you'll be better equipped to quickly and efficiently analyze numbers and find their factors. Remember, practice makes perfect!