When 121012 is divided by 12, the remainder is
2017
When 121012 is divided by 12, the remainder is
- A.
4
4 - B.
3
3 - C.
2
2 - D.
0
0
Attempted by 32 students.
Show answer & explanation
Correct answer: A
Key idea: use divisibility by 4 and 3 because 12 = 3 × 4.
Find remainder mod 4: look at the last two digits. 12 ÷ 4 has remainder 0, so the number is 0 mod 4.
Find remainder mod 3: sum the digits 1+2+1+0+1+2 = 7, and 7 ÷ 3 has remainder 1, so the number is 1 mod 3.
Find r (0 ≤ r < 12) with r ≡ 0 (mod 4) and r ≡ 1 (mod 3). Check multiples of 4: 0 → 0 mod 3, 4 → 1 mod 3. So r = 4.
Verification: 12 × 10084 = 121008, and 121012 − 121008 = 4, so the remainder is 4.
Answer: The remainder when 121012 is divided by 12 is 4.