Therefore it is 1.
Therefore it is 1.
Therefore it is 1.
Therefore it is 1.
Therefore it is 1.
The last digit is 4.
4.
6. All even powers of 4 end in 6
I assume you mean the last digit. The idea is to find a pattern: 8 to the power 1 ends with 8 8 to the power 2 ends with 4 8 to the power 3 ends with 2 (to figure this out, I just multiplied 4 x 8) 8 to the power 4 ends with 6 (once again, multiply the last digit of the previous power x 8) 8 to the power 5 ends with 8 8 to the power 6 ends with 4 ... As you can see, it all repeats, with a period of 4. Therefore, any exponent that is a multiple of 4 will end with 6. Find the nearest multiple of 4 that is smaller than 2015, then continue calculating - always with the last digit.
The digit with which a multiple of 4 ends depends on the last digit of the other factor. If the last digit is a zero, the product ends with zero; if the last digit is a 1, the product ends with 4; etc. The only options for the last digit of the product are 0, 2, 4, 6, 8.
The last digit is 4.
4.
133 to the power of 4 = 1334 = 133 x 133 x 133 x 133 = 312,900,721
The units' digit of 222 to the power 666 is 4.
6. All even powers of 4 end in 6
The last digit is 3. If you multiply 3 repeatedly by itself, you get the last digits:3, 9, 7, 1, 3, 9, 7, 1... In other words, every fourth power of 3 will end with the digit 1. Since any factorial starting at 4! has 4 as a factor, it follows that the last digit is 1.
4 x 4 = 16. If you multiply the last digit by 4: 6 x 4 = 24 (ends with 4). Continue multiplying by 4, and you see that the last digit will always alternate between 4 and 6 - 4 for the odd powers, and 6 for the even powers. So, in this case, the answer is 4.
I assume you mean the last digit. The idea is to find a pattern: 8 to the power 1 ends with 8 8 to the power 2 ends with 4 8 to the power 3 ends with 2 (to figure this out, I just multiplied 4 x 8) 8 to the power 4 ends with 6 (once again, multiply the last digit of the previous power x 8) 8 to the power 5 ends with 8 8 to the power 6 ends with 4 ... As you can see, it all repeats, with a period of 4. Therefore, any exponent that is a multiple of 4 will end with 6. Find the nearest multiple of 4 that is smaller than 2015, then continue calculating - always with the last digit.
The digit with which a multiple of 4 ends depends on the last digit of the other factor. If the last digit is a zero, the product ends with zero; if the last digit is a 1, the product ends with 4; etc. The only options for the last digit of the product are 0, 2, 4, 6, 8.
If the last two digits are divisible by 4. This is equivalent to: Last digit = 0, 4, 8 and the digit before (in tens place) is even or Last digit = 2 or 6 and the digit before (in tens place) is odd.
4
A 4 digit pin is the last four numbers in your phone number.