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Chapter 1: Q. 385R (page 90)

Use the divisibility test to determine whether 180 is divisible by2, by 3, by 5, by 6 and by 10.

Short Answer

Expert verified

The number 180 is divisible by the numbers 2, 3, 5, 6 and 10.

Step by step solution

01

Step 1. Divisibility test.

A number is divisible by:

  • 2 if the last digit is 0, 2, 4, 6, or 8.
  • 3 if the sum of the digits is divisible by 3.
  • 5 if the last digit is 5 or 0.
  • 6 if it is divisible by both 2 and 3.
  • 10 if it ends with 0.
02

Step 2. Apply the divisibility test.

Apply the divisibility test to find the number is divisible by 2 or not.

The number 180 is divisible by 2, because the last digit of the 180 is zero.

The number 180 is divisible by 2.

Apply the divisibility test check whether 180 is divisible by 3 or not.

The number 180 is divisible by 3, because the sum of the digits of 180(1+8+0=9) is divisible by 3.

Therefore, the number 180 is divisible by 3.

03

Step 3. Apply the divisibility test.

Apply the divisibility to check whether 180 is divisible by 5 or not.

The number 180 is divisible by 5, because the last digit of 180 is 0.

Therefore, the number 180 is divisible by 5.

Apply the divisibility to check whether 180 is divisible by 6 or not.

The number 180 is divisible by 6, because the number 180 is divisible by both 2 and 3.

Therefore, the number 180 is divisible by 6.

Apply the divisibility test to check whether 180 is divisible by 10 or not.

The number 180 is divisible by 10, because the number 180 ends with 0.

Therefore, the number 180 is divisible by 10.

04

Step 4. Conclusion.

The number 180 is divisible by the numbers 2, 3, 5, 6 and 10.

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