Calculate i, 5*7*9 (mod10) ii, 2^4 (mod7) iii, 6^2 (mod 9)?

Question

Could you also explain a little how to do the above 3 questions. Very grateful for any help. Thank You
Struggling maths student

Answer 1

5*7*9 (mod 10) means what is the remainder when you divide 5*7*9 by 10. 5*7*9=315 and 315/10 is equal to 31 with 5 left over. Therefore the answer would be 5. For the second one 2^4 (mod 7) means what is the remainder when you divide 2^4 by 7. 2^4= 16. 16/7 is 2 with a remainder of 2. Therefore this answer is 2. Finally 6^2(mod 9) means what is the remainder when you divide 6^2 by 9. 6^2=36 and 36/9=4 with no remainder. Therefore this answer is 0.

Answer 2

The mod is simply the remainder from the division.

i) You can substitute numbers with their modulo equivalents to make things simpler. In this case 7 can be replaced with -3 and 9 with -1 (same remainder when divided by 10):

5*7*9 (mod10)
= 5*(-3)*(-1) (mod 10)
= 15 (mod 10)
= 5 (mod 10)

Even easier: 5 * odd numbers will have 5 as its last digit, so the remainder when divided by 10 is 5. Simple as that.

The other two are simple, just calculate and figure out the remainder.

ii) 2^4 (mod7) = 16 (mod7) = 2 (mod7)
iii) 6^2 (mod9) = 36(mod9) = 0(mod9)

Answer 3

5*7*9 mod 10 = 315 mod 10 = 5

2^4 mod 7 = 16 mod 7 = 2

6^2 mod 9 = 36 mod 9 = 0

X mod Y = Remainder when X divided by Y.

Answer 4

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