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What is the sum of all prime numbers between 1 and 100 that are simultaneously one greater than a multiple of 4 and one less than a multiple of 5?
118
Start with the numbers that are 1 less than a multiple of 5.
This produces, 4, 9, 14, 19, 24,...,89, 94, 99
Clearly the sequence 4, 14, 24 etc has to be a multiple of 4 or 2 greater than a multiple of 4 so these do not apply.
This leaves 9,19,29,39,49,59,69,79,89,99.
The prime numbers within this group are, 19, 29, 59, 79 & 89.
The numbers that are 1 greater than a multiple of 4 are 29 & 89.
29 + 89 = 118.
Using Modular Arithmetic we have :
x ≡ 1 (mod4),
x = -1 ≡ 4 (mod5) so we can write that, x = 5n + 4... (where n is a positive integer)
Thus, 5n + 4 ≡ 1 (mod4) : 5n ≡ -3 ≡ 1 (mod4) : 4n + n ≡ n ≡ 1 (mod4)
Consequently n = 1,5,9,13,17...
As, x = 5n + 4 , then x = 9, 29, 49, 69, 89.
Of these, only 29 & 89 are prime numbers. Hence, 29 + 89 = 118
What else can I help you with?
What are the square numbers that are greater than 80 and a multiple of 16?
There are infinitely many of them. The square of any multiple of four that is greater or equal to 12 will meet the requirement.
What is the numbers that greater than 400 but is a multiple of 9?
405 = 9 x 45
What is The multiple of 9 is in between two prime numbers?
The multiples of 9 are numbers that can be divided evenly by 9. The two prime numbers closest to a multiple of 9 are 7 and 11. Since 9 is between 7 and 11, the multiple of 9 that is in between these two prime numbers is 9 itself.
What 3 numbers GCF is 12 with one of the numbers being greater than 100?
12, (any multiple of 12 less than 100), any multiple of 12 greater than 100) Example: 12, 24, and 108
What numbers between 61 and 107 are a multiple of 8?
64,72,80,88,96,104 :)
What Numbers between 55 and 101 that has a multiple 2810?
what numbers between 55 and 101 that has a multiple of 2,8,10
When is the least common multiple of a pair of numbers that number?
When one of the numbers is a multiple of the other, the greater is the LCM and the lesser is the GCF of that set.
Is every multiple of a number is always greater then the number itself?
Not with negative numbers. -10 is a multiple of -2.
What is the LCM of 2 numbers when one is a multiple of the other?
The greater number.
Is a multiple always greater than the number?
No, not when negative numbers are involved. For example, -2 is a multiple of both -1 and 1 and is not greater than either.
What is The least common multiple of 2 numbers if one number is a multiple of the other?
The LCM is the greater number.
The LCM of two consecutive numbers is greater then 200 and is a multiple of 7. What are the two numbers?
14 and 15
Is it true that when one number is multiple of another the greatest common factor of the numbers is greater of the numbers?
No, the lesser.
What are the square numbers that are greater than 80 and a multiple of 16?
There are infinitely many of them. The square of any multiple of four that is greater or equal to 12 will meet the requirement.
Lcm of two consecutive numbers is greater than 200 and is a multiple of 7?
To find the least common multiple (LCM) of two consecutive numbers that is greater than 200 and is a multiple of 7, we need to consider the properties of consecutive numbers and multiples of 7. Since the LCM must be greater than 200 and a multiple of 7, the two consecutive numbers must be 28 and 29. The LCM of 28 and 29 is 812, which is greater than 200 and a multiple of 7.
LCM of two numbers if one number is a multiple of the other?
the greater of the two.
What numbers between 55101 are a multiple 2816?
There can be no numbers between a single number: 55101.
