Let us take 8560. Does it have any factors from 2 to 10 (2, 3, 4, 5, ..., 9, 10)?

Question

Homi · Accepted Answer

We will use divisibility rules to check each number.

Step 1 — Check for 2

We look at the last digit. The last digit of 8560 is 0. 0 is an even number. So, 8560 can be divided by 2.

$\boxed{\text{Yes, 2 is a factor}}$

Step 2 — Check for 3

We add all the digits. The sum of digits is: $8 + 5 + 6 + 0$ $= 19$ 19 cannot be divided by 3. So, 8560 cannot be divided by 3.

$\boxed{\text{No, 3 is not a factor}}$

Step 3 — Check for 4

We look at the last two digits. The last two digits are 60. We divide 60 by 4. $60 \div 4$ $= 15$ 60 is divisible by 4. So, 8560 can be divided by 4.

$\boxed{\text{Yes, 4 is a factor}}$

Step 4 — Check for 5

We look at the last digit. The last digit of 8560 is 0. Numbers ending in 0 or 5 are divisible by 5. So, 8560 can be divided by 5.

$\boxed{\text{Yes, 5 is a factor}}$

Step 5 — Check for 6

A number is divisible by 6 if it is divisible by 2 and 3. 8560 is divisible by 2. 8560 is not divisible by 3. So, 8560 cannot be divided by 6.

$\boxed{\text{No, 6 is not a factor}}$

Step 6 — Check for 7

We divide 8560 by 7. $8560 \div 7$ $= 1222 \text{ with a leftover of } 6$ There is a leftover. So, 8560 cannot be divided by 7.

$\boxed{\text{No, 7 is not a factor}}$

Step 7 — Check for 8

We look at the last three digits. The last three digits are 560. We divide 560 by 8. $560 \div 8$ $= 70$ 560 is divisible by 8. So, 8560 can be divided by 8.

$\boxed{\text{Yes, 8 is a factor}}$

Step 8 — Check for 9

We add all the digits. The sum of digits is: $8 + 5 + 6 + 0$ $= 19$ 19 cannot be divided by 9. So, 8560 cannot be divided by 9.

$\boxed{\text{No, 9 is not a factor}}$

Step 9 — Check for 10

We look at the last digit. The last digit of 8560 is 0. Numbers ending in 0 are divisible by 10. So, 8560 can be divided by 10.

$\boxed{\text{Yes, 10 is a factor}}$

Answer

(i) Yes, 8560 has factors from 2 to 10. (ii) The factors are 2, 4, 5, 8, and 10.

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