Understanding Divisibility by 71

The question asks us to identify which of the given numbers is perfectly divisible by 71. This means we need to find the number that, when divided by 71, results in a whole number with no remainder.

Checking Each Option for Divisibility by 71

We will test each option by performing the division:

• Option 1: 5609
  To check if 5609 is divisible by 71, we perform the division:

  $$ \frac{5609}{71} $$

  Let's calculate:

  $$ 71 \times 70 = 4970 $$

  $$ 5609 - 4970 = 639 $$

  Now, let's see how many times 71 goes into 639:

  $$ 71 \times 9 = 639 $$

  So, $5609 = 71 \times 79$. Since the division results in a whole number (79) with no remainder, 5609 is divisible by 71.

• Option 2: 6121
  To check if 6121 is divisible by 71, we perform the division:

  $$ \frac{6121}{71} $$

  Let's calculate:

  $$ 71 \times 80 = 5680 $$

  $$ 6121 - 5680 = 441 $$

  Now, let's see how many times 71 goes into 441:

  $$ 71 \times 6 = 426 $$

  The remainder is $441 - 426 = 15$. So, $6121 = 71 \times 86 + 15$. Since there is a remainder, 6121 is not divisible by 71.

• Option 3: 6010
  To check if 6010 is divisible by 71, we perform the division:

  $$ \frac{6010}{71} $$

  Let's calculate:

  $$ 71 \times 80 = 5680 $$

  $$ 6010 - 5680 = 330 $$

  Now, let's see how many times 71 goes into 330:

  $$ 71 \times 4 = 284 $$

  The remainder is $330 - 284 = 46$. So, $6010 = 71 \times 84 + 46$. Since there is a remainder, 6010 is not divisible by 71.

• Option 4: 5603
  To check if 5603 is divisible by 71, we perform the division:

  $$ \frac{5603}{71} $$

  Let's calculate:

  $$ 71 \times 70 = 4970 $$

  $$ 5603 - 4970 = 633 $$

  Now, let's see how many times 71 goes into 633:

  $$ 71 \times 8 = 568 $$

  The remainder is $633 - 568 = 65$. So, $5603 = 71 \times 78 + 65$. Since there is a remainder, 5603 is not divisible by 71.

Conclusion: Identifying the Divisible Number

After checking all the options, we found that only 5609 results in a whole number when divided by 71.