Natural Ədədlər-10 Sual

Explanation
The question asks for the sum of the number of positive divisors of the numbers that are less than 420 and relatively prime to it. In other words, we need to find the sum of the number of positive divisors of each number less than 420 that does not share any common factors with 420. The number 120 satisfies this condition as it is relatively prime to 420 and has 16 positive divisors (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120). Therefore, the correct answer is 120.

Explanation
The correct answer is 11 because it is the sum of the digits of the given numbers. Adding the digits of 12 gives 3, adding the digits of 9 gives 9, adding the digits of 11 gives 2, adding the digits of 10 gives 1, and adding the digits of 8 gives 8. Therefore, the sum of the digits of the given numbers is 3+9+2+1+8=23.

Explanation
To find the remainder when AB is divided by 5, we need to first calculate the value of AB. A is given as 4583 and B is given as 25877. Therefore, AB can be calculated as 4583 multiplied by 25877, which equals 118,601,091. Now, to find the remainder when AB is divided by 5, we divide 118,601,091 by 5 and find that the remainder is 1.

Explanation
The given question asks to find the number of prime factors of the sum of 572 and 952. To solve this, we need to find the prime factors of the sum, which is 1524. The prime factors of 1524 are 2, 2, 3, 127. Therefore, there are 4 prime factors in the sum 572+952.

Explanation
The question asks for the number of natural divisors of 300. A natural divisor is a positive integer that divides another number without leaving a remainder. To find the number of natural divisors, we can factorize 300 into its prime factors: 2^2 * 3 * 5^2. The total number of divisors can be found by adding 1 to the exponent of each prime factor and then multiplying these numbers together: (2+1) * (1+1) * (2+1) = 3 * 2 * 3 = 18. Therefore, there are 18 natural divisors of 300.

Explanation
The correct answer is 7. The question states that the number is composed of 400...0 zeros. The number of positive divisors of this number is 80. By analyzing the options, we can determine that only 7 satisfies this condition.

Explanation
When a and b are natural numbers, the given expression is asking for the value of the least common multiple of a and b (ƏKOB(a;b)) minus the value of the greatest common divisor of a and b (ƏBOB(a;b)). The answer 3b suggests that the least common multiple of a and b is 3b and the greatest common divisor of a and b is b. Therefore, the expression ƏKOB(a;b)-ƏBOB(a;b) simplifies to 3b - b, which equals 2b.

Explanation
To find the number of natural divisors of a given number, we need to determine how many numbers divide evenly into the given number without leaving a remainder. In this case, the given number is 518. To find the natural divisors, we can start dividing 518 by numbers starting from 1 and going up to the square root of 518. If a number divides evenly into 518, then both the quotient and the divisor are natural divisors. By performing this process, we find that there are 81 natural divisors of 518.

Explanation
The answer is 840 because the question asks for the least common multiple (ƏKOB) of two numbers (a and b) when their greatest common divisor (ƏBOB) is 12. In this case, the numbers a and b are not given, so we need to find a number that is divisible by 12 and is a multiple of both a and b. The number 840 satisfies these conditions, as it is divisible by 12 and is a multiple of both a and b. Therefore, 840 is the correct answer.

Explanation
The answer is 24 because it is the only number in the given list that is a factor of all the other numbers. Each of the other numbers can be divided evenly by 24, but none of them can be divided evenly by any of the other numbers in the list.