What is the remainder when (2^16)(3^16)(7^16) is divided by 10?
A. 0
B. 2
C. 4
D. 6
E. 8
Source: Veritas
Answer: D
A. 0
B. 2
C. 4
D. 6
E. 8
Source: Veritas
Answer: D
Key concept: (x^n)(y^n)(z^n) = (xyz)^nBTGModeratorVI wrote: ↑Tue Feb 18, 2020 11:02 amWhat is the remainder when (2^16)(3^16)(7^16) is divided by 10?
A. 0
B. 2
C. 4
D. 6
E. 8
Source: Veritas
Answer: D
So, we can write: (2^16)(3^16)(7^16) = (2 x 3 x 7)^16
= (42)^16
At this point we need only find the unit's digit of (42)^16
42¹ = 42
42² = ---4
42³ = ---8
42⁴ = ---6
42⁵ = ---2
42 has a cycle of 4 (the units digit repeats every 4 powers)
This means 42^8 = ---6, 42^12 = ---6, 42^16 = ---6, etc
Since 42^16 = ---6, we can conclude that 42^16, when divided by 10, will leave a remainder of 6
Answer: D
Cheers,
Brent
