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Q: What is the sum of all the positive divisors of 72?

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72 is an abundant number because the sum of its positive divisors, not including 72 itself, is larger than 72. Positive divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 = 123 > 72 (if an integer is larger than the sum of its positive divisors , not including the integer itself, then that integer is called a deficient number, such as prime or power of prime numbers or numbers like 10 are).

72 is an abundant number because the sum of its positive divisors, not including 72 itself, is larger than 72. Positive divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 = 123 > 72 (if an integer is larger than the sum of its positive divisors , not including the integer itself, then that integer is called a deficient number, such as prime or power of prime numbers or numbers like 10 are).

Here are the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Some people leave 1 and/or the number itself out when totaling. I'll leave that up to you.

The sum of the positive whole-number factors of 30 is 72.

62 + 72 = 85

The greatest common factor of 42 and 72 is 6 Gcf stands for Greatest Common Factor, The gcf of 42 and 72 is the largest positive number that is a factor of both 42 and 72. The positive factors of 42 (the integral divisors of 42) are: 1, 2, 3, 6, 7, 14, 21, and 42. The positive factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 36, and 72. Therefore the gcf of 42 and 72 is 6, as the greatest factor that 42 and 72 have in common.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

72.

the sum is 72

22

The sum of 72 and 12 is 84. The product of the two numbers is 864.

72, 36 and 1

1, 36 and 72

The sum of 84 and 72 is 156.

The sum of 72 and 144 is 216.

It is: 72+2*(25) = 125

(ITS 60. Factors: 1,2,3,4,5,6,10,12,15,20,30,60) The smallest positive integer with 12 divisors, including 1 and itself, is 60. They are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Notice that six of these divisors are smaller than the square-root of 60, and six of them are larger. (Only a number that is a perfect square can have an odd number of divisors, incidentally.)How can you find this result? To find quickly the number of divisors in any positive integer, first factorise it into prime factors, using exponents to count repetitions. Let's use 72 as an example: 72 = 8 X 9 = 2³ X 3². Thus, 3 occurs twice, and 2 occurs thrice. Every divisor of 72 contains 3 as a factor 0, 1, or 2 times; and it contains 2 as a factor either 0, 1, 2, or 3 times; and it can contain no other prime factor besides 2 and 3. Because there are 3 choices of how many times the divisor of 72 may contain 3 as a factor and 4 choices of how many times it may contain 4 as a factor, there are twelve possible divisors of 72. You can check this by asking how many divisors 72 has that are less than 9, the smallest positive integer whose square is greater than 72. It turns out that there are six, namely, 1, 2, 3, 4, 6, and 8. Its other six divisors must be at least 9, and they are found, by division, to be 9, 12, 18, 24, 36, and 72.Applying this logic, we now seek the smallest positive integer with twelve divisors: We can readily see that the number we seek will be a product of powers of the smallest primes. Moreover, it is plausible, even before multiplying it out, that it will be either the product of 2² X 3 X 5 or the product of 2³ X 3². And why is this? If we use 2² X 3 X 5, each of its divisors must present us 3 X 2 X 2 = 12 choices, as to the number of times each of its prime factors may be repeated in its prime factorization (obtained by adding 1 to each of the exponents and taking their product - noting that 1 is the exponent of 3 and 5, whilst 2 is the exponent we have shown for 2). Therefore, it will have 12 divisors. If we use 2³ X 3², each of its divisors must present us 4 X 3 = 12 choices, obtained by the same method.We can easily see that 2^11 (giving us 12 choices and, therefore, 12 divisors) is going to be much too large. On the other hand, four or more distinct prime factors (such as 2, 3, 5, and 7) will present us with with at least 2^4 choices and 2^4 = 16 divisors, which is more than we need. Now, since we can readily see that 2² X 3 X 5 = 60 is smaller than 2³ X 3² = 72, it is clear that 60 is the number we seek.

-72 + 7 = -65

The sum is: 72+9 = 81

90

195

8838.

72

153