Divisibility - practice problems
Divisibility concerns whether one integer can be divided by another with no remainder, written as a|b (a divides b) when b/a is an integer. Divisibility rules provide shortcuts: a number is divisible by 2 if even, by 3 if digit sum is divisible by 3, by 5 if ending in 0 or 5, by 9 if digit sum is divisible by 9, and so on. Understanding divisibility is essential for factoring, finding greatest common divisors (GCD), least common multiples (LCM), and simplifying fractions. Divisibility properties include transitivity and compatibility with arithmetic operations. These concepts underpin number theory, modular arithmetic, and have applications in scheduling, patterns, and cryptography. Testing divisibility helps identify factors and prime numbers efficiently.Number of problems found: 436
- Division with a remainder
Find the least number which when divided by 8, 12, and 20 leaves a remainder of 5 in each case. - The product 18
The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers. - The remainder 3
The remainder is 31 when dividing a number by 45. What would the remainder be if the same number were divided by 15? - 4th digit Write a digit in place of X so that 85X634 is divisible by 11.
- The remainder
Find the remainder if 17²00 is divided by 18. - Tailors
Find the largest number of tailors who can share either 48m or 12m of fabric equally without a reminder? - Factorial divisible by 75 Find the least positive integer n such that n! is divisible by 75.
- Consecutive odd numbers
Find three consecutive odd numbers whose sum is 93. - Add five to lcm The least number, which, when diminished by 5, is divisible by each of 21, 28, 36, and 45.
- LCM and HCF 2 If the product of two numbers is 5780 and their HCF is 17, then what is their LCM?
- Remainder one Find the least number when divided by 2,3,4,5,6, and 7, leaving the remainder as 1 in each case.
- Divisible by three What least value must be assigned to the unknown x so that the number 789x563 is divisible by 3?
- Arithmetic progressions.
Find the sum of all the numbers between 9 and 204, which is exactly divisible by 3. - Relay teams
There are 159 students to be grouped into relay teams. Each team should have the same number of students. Can each team have 3,5 or 6 students? Explain. - A number 8 A number K is such that when it is divided by 27, 30, or 45, the remainder is 3. Find the smallest possible value of K
- Same remainder
Find the greatest number that will divide 43, 91, and 183 so as to leave the same the remainder in each case. - Two pieces 2
Two pieces of length 12/5 m and 23/9 m are cut from a rope of length 13 m. Find the length of the remaining rope. - Unknown number 35 I am a number between 121 and 149. I can be divided by both 3 and 5. What number am I?
- Beekeeper 2
The beekeeper has more than 190 kilos of honey and less than 200 kilos. If he divides it into 8-kilogram bottles, he rest 3 kilos. If he divides it into 7-kilogram bottles, he he rest kilos. How many kilos of honey does he have? - All zeros
How many zeros does the product of the numbers 10.11.12.13.14.15.20.21.22.23.24.25 end with?
Do you have unsolved math question and you need help? Ask a question, and we will try to solve it. We solve math question.
