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Remember:-
1. Last Digit of any [Even Number] ^ 4n = 6
Last Digit of any [Odd Number] ^ 4n = 1
2. [25]^n always ends with 25.
[76]^n always end with 76.
3. Perfect Number: -
A number is a perfect number when sum of all its factors excluding number itself equals to number.
Eg. 6 Factors à 1, 2, 3 and 6
Ie 1 + 2 + 3 = 6
28, 496 and 8128 are few of such numbers.
4. Consider a number formed with digit a and b ie ab then number formed by reversing the digit with be ba then
ab = 10 a+ b
ba = 10 b + a
The perfect number note is a good memory hook, since it forces students to list factors — 1+2+3=6 for 6, and 1+2+4+7+14=28 for 28. It is also worth mentioning that every known perfect number is even and tied to a Mersenne prime by the Euclid-Euler theorem, which makes a nice teaser for curious students. On point 5, the product of three consecutive numbers is divisible by 3, but it is also always divisible by 6 — one of the three is even and one is a multiple of 3. Full disclosure: I run factorcalculator.org, a free factor/LCM calculator site, which lists all the factors of a number — handy for verifying perfect-number sums like these.
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