The digit in the unit place of the number 6^129 × 7^307 is

(a) 2
(b) 4
(c) 8 ✓ UPSC's answer
(d) 6

Why the answer is (c)

• The unit digit of 6 raised to any positive integer power is always 6, so the unit digit of 6^129 is 6.

• The unit digits of powers of 7 follow a repeating cycle of 4: 7, 9, 3, 1.

• To find the unit digit of 7^307, divide the exponent 307 by 4, which gives a remainder of 3.

• The 3rd number in the cycle (7, 9, 3, 1) is 3, so the unit digit of 7^307 is 3.

• Multiply the unit digits of the two factors: 6 × 3 = 18.

• The unit digit of the product is 8, which corresponds to option (c).

Why the other options are wrong

(a) 2: Option (a) is incorrect because the unit digit of the product is 8, not 2.
(b) 4: Option (b) is incorrect because the unit digit of the product is 8, not 4.
(d) 6: Option (d) is incorrect because the unit digit of the product is 8, not 6.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.