Divisibility - high school - practice problems - page 2 of 4
Number of problems found: 69
- Determine 8611
Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product. - Justification 8468
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - Three-digit integers
How many three-digit natural numbers exist that do not contain zero and are divisible by five? - Three numbers
We have three different non-zero digits. We will create all three digits numbers from them to use all three figures in each. We add all the made numbers and get the sum of 1554. What were the numbers?
- The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Three-digit 7248
Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number. - Notation 7014
There is no 0 in the decimal notation in natural numbers, and there are even numbers or odd numbers, each at least once. Find the number of all k-digit natural numbers. - Inverted nine
In the hotel Inverted Nine, each hotel room number is divisible by 6. How many rooms can we count with the three-digit number registered by digits 1,8,7,4,9?
- PIN code
The PIN on Michael's credit card is a four-digit number. Michael told his friend: • It is a prime number - a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second digit is gre - Divisible 6615
How many 3-digit numbers can be composed of the digit 1,3,5,7,9 if the digits are not allowed to be repeated in the number notation? How many of them are divisible by five? - The sum 2
The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer. - Candy and boxes
We have some candy and empty boxes. When we put ten sweets in boxes, there will be two candies and eight empty boxes left. When of eight, there will be six candies and three boxes left. How many candy and empty boxes are gone when we put nine sweets into - Big number
What is the remainder when dividing 10 by 9 to 47 - 111?
- Cuboid walls
Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm². - Expression 4451
Find the largest natural number d that has that property for any natural number the number n is the value of the expression V (n) = n ^ 4 + 11n²−12 is divisible by d. - Modulo
Find x in the modulo equation: 47x = 4 (mod 9) Hint - read as what number 47x divided by 9 (modulo 9) give remainder 4. - Infinite decimal
Imagine the infinite decimal number 0.99999999... That is a decimal and her endless series of nines. Determine how much this number is less than the number 1. Thank you in advance. - Permutations
How many 4-digit numbers can be composed of numbers 1,2,3,4,5,6,7 if: and the digits must not be repeated in the number b, the number should be divisible by five, and the numbers must not be repeated c, digits can be repeated
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