- What is the largest perfect number?
- Can a prime number be a perfect number?
- What is the smallest odd abundant number?
- What are divisors of 21?
- Is 77 abundant or deficient?
- Is 8128 a perfect number?
- What is the most perfect number?
- How do you tell if a number is abundant deficient or perfect?
- IS 120 a perfect number?
- What is the weirdest number?
- Is 22 a deficient number?
- What factors do prime numbers always have?
- Is 26 abundant deficient or perfect?
- Are all prime numbers deficient?
- How do you find a deficient number?
- What is a number divisible by 3?
- What does the number 120 mean?
- Is 26 a deficient number?
- Are there any odd abundant numbers?
- Why is 28 the perfect number?
- What is the only positive prime number?

## What is the largest perfect number?

BLOWING ROCK, NC, December 21, 2018 — The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 282,589,933-1, having 24,862,048 digits.

A computer volunteered by Patrick Laroche made the find on December 7, 2018..

## Can a prime number be a perfect number?

If a prime number can be written as 2n – 1 for some n, the prime number is a Mersenne prime. If the sum of divisors of a number (excluding the number itself) equals the number, the number is a perfect number. Perfect numbers are related to Mersenne primes.

## What is the smallest odd abundant number?

PropertiesThe smallest odd abundant number is 945.The smallest abundant number not divisible by 2 or by 3 is 5391411025 whose distinct prime factors are 5, 7, 11, 13, 17, 19, 23, and 29 (sequence A047802 in the OEIS).

## What are divisors of 21?

The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and 7 is also a divisor of 21).

## Is 77 abundant or deficient?

What is the list of divisors from 1 to 100?NumberList of DivisorsDivisors of 771,7,11,77Divisors of 781,2,3,6,13,26,39,78Divisors of 791,79Divisors of 801,2,4,5,8,10,16,20,40,8096 more rows

## Is 8128 a perfect number?

8128 is the integer following 8127 and preceding 8129. It is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 127, 27 – 1, with 26 (27 – 1) yielding 8128.

## What is the most 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. The discovery of such numbers is lost in prehistory.

## How do you tell if a number is abundant deficient or perfect?

If P(n) > n, then n is called an abundant number. If P(n) < n, then n is called a deficient number. If P(n) = n, then n is called a perfect number.

## IS 120 a perfect number?

120 is the first multiply perfect number of order three (a 3-perfect or triperfect number). The sum of its factors (including one and itself) sum to 360; exactly three times 120. … However, there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number.

## What is the weirdest number?

Examples. The smallest weird number is 70. Its proper divisors are 1, 2, 5, 7, 10, 14, and 35; these sum to 74, but no subset of these sums to 70. The number 12, for example, is abundant but not weird, because the proper divisors of 12 are 1, 2, 3, 4, and 6, which sum to 16; but 2 + 4 + 6 = 12.

## Is 22 a deficient number?

(number theory) A number that is greater than the sum of all of its divisors except itself. The factors of 22 are 1, 2 and 11 and 22, and 1 + 2 + 11 = 14, which is less than 22, so 22 is a deficient number.

## What factors do prime numbers always have?

A prime number is an integer, or whole number, that has only two factors — 1 and itself. Put another way, a prime number can be divided evenly only by 1 and by itself. Prime numbers also must be greater than 1. For example, 3 is a prime number, because 3 cannot be divided evenly by any number except for 1 and 3.

## Is 26 abundant deficient or perfect?

The Integers 1 to 100NDivisors of NNotes241, 2, 3, 4, 6, 8, 12, 24Abundant251, 5, 25Deficient261, 2, 13, 26Deficient271, 3, 9, 27Deficient65 more rows

## Are all prime numbers deficient?

Any prime number is deficient, because it has only one proper factor: 1. All numbers of the form 2n are also deficient. Example: 32 (=25) is a deficient number because the sum of its distinct proper factors is 31 (1+2+4+8+16).

## How do you find a deficient number?

A number n is said to be Deficient Number if sum of all the divisors of the number denoted by divisorsSum(n) is less than twice the value of the number n. And the difference between these two values is called the deficiency. The first few Deficient Numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19 …..

## What is a number divisible by 3?

Numbers Divisible by 3. Numbers are divisible by 3 if the sum of all the individual digits is evenly divisible by 3. For example, the sum of the digits for the number 3627 is 18, which is evenly divisible by 3 so the number 3627 is evenly divisible by 3.

## What does the number 120 mean?

120 is a creative and independent number. The energy the number 120 represents resonates with creative expression — highly creative. … Although comfortable being alone, it’s also a social energy. The energy includes imagination, effective communication, tolerance, joyfulness, optimism, and dynamism.

## Is 26 a deficient number?

Examples. The first few deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, … (sequence A005100 in the OEIS)

## Are there any odd abundant numbers?

An abundant number is a number whose proper divisors sum to a value greater than itself. After 945, the odd-abundant numbers are 1,575, 2,205, 2,835, 3,465, … … There are also abundant numbers whose proper divisors have a sum greater than twice the original number.

## Why is 28 the perfect number?

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. … For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28.

## What is the only positive prime number?

An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. For example, the prime divisors of 10 are 2 and 5, and the first six primes are 2, 3, 5, 7, 11, and 13.