It is easy to check if some of these numbers are factors or not without doing long division. Can you find them?

Question

Homi · Accepted Answer

We use special rules to check if a number divides another number without long division.

Let us consider the number 120. We will check if 2, 3, 4, 5, 6, 7, 8, 9, 10 are its factors.

Step 1 — Check for 2

We want to see if 2 is a factor of 120. A number can be divided by 2. Its last digit must be an even number. Even numbers are 0, 2, 4, 6, 8. The last digit of 120 is 0. 0 is an even number. So, 2 is a factor of 120.

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

Diagram 1

Step 2 — Check for 3

We want to see if 3 is a factor of 120. A number can be divided by 3. Its digits must add up to a multiple of 3. The digits of 120 are 1, 2, 0. Let us add these digits.

$1 + 2 + 0$

$= 3$

3 is a multiple of 3. So, 3 is a factor of 120.

$\boxed{\text{3 is a factor}}$

Step 3 — Check for 4

We want to see if 4 is a factor of 120. A number can be divided by 4. Its last two digits must form a number. This number must be divided by 4. The last two digits of 120 are 20. We check if 20 can be divided by 4.

$20 \div 4$

$= 5$

20 can be divided by 4. So, 4 is a factor of 120.

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

Step 4 — Check for 5

We want to see if 5 is a factor of 120. A number can be divided by 5. Its last digit must be 0 or 5. The last digit of 120 is 0. So, 5 is a factor of 120.

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

Step 5 — Check for 6

We want to see if 6 is a factor of 120. A number can be divided by 6. It must be divided by both 2 and 3. From Step 1, 120 can be divided by 2. From Step 2, 120 can be divided by 3. Both conditions are true. So, 6 is a factor of 120.

$\boxed{\text{6 is a factor}}$

Step 6 — Check for 7

We want to see if 7 is a factor of 120. Let us use the divisibility rule for 7. Take the last digit. Double this last digit. Subtract it from the rest of the number. The number is 120. The last digit is 0. Double the last digit: $2 \times 0 = 0$ . The rest of the number is 12. Subtract the doubled digit from the rest.

$12 - 0$

$= 12$

12 cannot be divided by 7. It leaves a leftover. So, 7 is not a factor of 120.

$\boxed{\text{7 is not a factor}}$

Step 7 — Check for 8

We want to see if 8 is a factor of 120. A number can be divided by 8. Its last three digits must form a number. This number must be divided by 8. The last three digits of 120 form 120. We check if 120 can be divided by 8.

$120 \div 8$

$= 15$

120 can be divided by 8. So, 8 is a factor of 120.

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

Step 8 — Check for 9

We want to see if 9 is a factor of 120. A number can be divided by 9. Its digits must add up to a multiple of 9. The digits of 120 are 1, 2, 0. Let us add these digits.

$1 + 2 + 0$

$= 3$

3 is not a multiple of 9. So, 9 is not a factor of 120.

$\boxed{\text{9 is not a factor}}$

Step 9 — Check for 10

We want to see if 10 is a factor of 120. A number can be divided by 10. Its last digit must be 0. The last digit of 120 is 0. So, 10 is a factor of 120.

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

Answer

(i) 2 is a factor of 120. (ii) 3 is a factor of 120. (iii) 4 is a factor of 120. (iv) 5 is a factor of 120. (v) 6 is a factor of 120. (vi) 7 is not a factor of 120. (vii) 8 is a factor of 120. (viii) 9 is not a factor of 120. (ix) 10 is a factor of 120.

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