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Question

Determine whether 75689604 is divisible by 2,4or 8


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Solution

Step 1 - Checking the divisibility by 2

A number is divisible by 2 if its last ( unit’s) digit is divisible by 2 I.e., if its last digit is 0,2,4,6,8

The given number has 4 in its unit's place , which is divisible by 2 2×2=4

Therefore 75689604 is divisible by 2

Step 2 - Checking the divisibility by 4

A number is divisible by 4 if the number formed by its last two ( unit’s and ten’s ) digits is divisible by 4.

The number formed by last two digits of 75689604 is 04 i.e., 4 which is divisible by 4 4×1=4

Therefore 75689604 is divisible by 4

Step 3 - Checking the divisibility by 8

A number is divisible by 8 if the number formed by its last three ( unit’s , ten’s and hundred’s ) digits is divisible by 8.

The number formed by last three digits of 75689604 is 604 which is not divisible by 8.

Therefore 75689604 is not divisible by 8

Hence , 75689604 is divisible by 2,4 but not divisible by 8


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