Understanding Divisibility by 8

This solution explains how to determine which number from the given options is divisible by 8. We will use the standard divisibility rule for 8.

Divisibility Rule for 8 Explained

A number is considered divisible by 8 if the number formed by its last three digits is also divisible by 8. If the last three digits form a number that leaves a remainder when divided by 8, then the original number is not divisible by 8.

Mathematically, if a number N can be represented as $N = 1000a + b$, where 'b' represents the number formed by the last three digits, then since $1000$ is divisible by 8 ($1000 = 8 \times 125$), the divisibility of N by 8 depends solely on the divisibility of 'b' by 8.

Checking Each Option

Let's apply the divisibility rule for 8 to each of the provided numbers:

Option 1: 18718

• The last three digits are 718.
• We check if 718 is divisible by 8.
• Calculation: $718 \div 8$
• $718 = 8 \times 89 + 6$
• Since there is a remainder of 6, 18718 is not divisible by 8.

Option 2: 18716

• The last three digits are 716.
• We check if 716 is divisible by 8.
• Calculation: $716 \div 8$
• $716 = 8 \times 89 + 4$
• Since there is a remainder of 4, 18716 is not divisible by 8.

Option 3: 18712

• The last three digits are 712.
• We check if 712 is divisible by 8.
• Calculation: $712 \div 8$
• $712 = 8 \times 89 + 0$
• Since the remainder is 0, 712 is divisible by 8. Therefore, 18712 is divisible by 8.

Option 4: 18714

• The last three digits are 714.
• We check if 714 is divisible by 8.
• Calculation: $714 \div 8$
• $714 = 8 \times 89 + 2$
• Since there is a remainder of 2, 18714 is not divisible by 8.

Conclusion on Divisibility

By applying the divisibility rule for 8, we found that the number formed by the last three digits of 18712 (which is 712) is divisible by 8. Thus, 18712 is the number divisible by 8 among the given options.