Q. What makes a number a perfect number?
Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.
Q. Why are perfect numbers important?
The primes are a good example. After noticing the primes then one can show the prime factorization theorem. Primes can be used to design a cryptographical system (RSA) powerful enough to protect many financial transactions at the current time. Perfect numbers create a “playground” for the interested.
Q. Is 8128 an amicable number?
amicable if each of them is the sum of all proper divisors of the other. they are called perfect numbers, otherwise they form an amicable pair. The first perfect numbers 6, 28, 496, 8128, and the smallest amicable pair 220, 284, were known to the Greek mathematicians.
Q. What is meant by amicable numbers?
…“amicable numbers”: two numbers are amicable if each is equal to the sum of the proper divisors of the other (for example, 220 and 284). Attributing virtues such as friendship and justice to numbers was characteristic of the Pythagoreans at all times.
Q. Are 1 and 2 amicable numbers?
The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.
Q. What is the smallest positive number with the property such that the sum of the cubes of its digits is not divisible by the sum of its digits?
91 = 63 + (-5)3 = 43 + 3. Numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways have been dubbed “taxicab numbers”….1729 (number)
| ← 1728 1729 1730 → | |
|---|---|
| Divisors | 1, 7, 13, 19, 91, 133, 247, 1729 |
| Greek numeral | ,ΑΨΚΘ´ |
| Roman numeral | MDCCXXIX |
| Binary | 110110000012 |
Q. How many number are there in which the number and its cube are same?
three numbers
Q. Who discovered the first pair of amicable numbers?
Pythagoras
Q. Is 78 a happy number?
The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100.
