Prime numbers - practice problems
A prime number is a natural number greater than 1 that has exactly two distinct divisors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, and they continue infinitely as proven by Euclid over 2000 years ago. The number 2 is the only even prime; all other primes are odd. The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either prime or can be uniquely expressed as a product of primes. Prime numbers are central to number theory, cryptography (especially RSA encryption), and have applications in computer science and mathematics. Methods for identifying primes include trial division, the Sieve of Eratosthenes, and more advanced primality tests.Number of problems found: 520
- Shipping problem
Paul works in the shipping department of a toy company. He sends toys in boxes each in the shape of a rectangular prism. The boxes' lengths, widths, and heights are whole numbers in inches. Paul needs a box with a total volume of 24 cubic inches. Find one - Circular track 3
Henry and Margo both began traveling around a circular track. Henry is riding his bike, and Margo is walking. It takes Henry 7 minutes to make it all the way around, and Margo takes 12 minutes. How many minutes will pass until they meet at the starting li - The ratio 22
The ratio of two numbers is 5 : 4 and their LCM is 800. Find the sum of numbers . - A,B and
A, B and C invested a capital in a ratio of 1/3:1/4:1/5. After 4 months A withdraws half of his capital. If the yearly profit is Rs 8470, find the share of A . - The sum 53
The sum ofthree numbers of a GP series is 35 and their product is 1000. Find the numbers. - A person 3
A person distributes his pens among four friends A, B, C and D in the ratio 1/3 : 1/4 : 1/5 : 1/6. What is the minimum number of pens that the person should have? - Beeps
An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The next time, when they will beep together at the earliest? - 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 sum 50
The sum of five consecutive integers is 385. Which one of these five integers is prime? - LCM and HCF 3 LCM of two integers is 1237. What is their HCF?
- The number 88 Write the number 88 as a product of prime factors.
- Divisor of two numbers Find the (greatest common) divisor of 18 and 45.
- The difference 9 The difference of two numbers is 20 and their product is 56.25 times their difference. Find the LCM of the numbers.
- Joseph 2
Joseph visits the club on every fifth day, Harry visits on every 24th day, and Susan visits on every ninth day. If all three of them met at the club on a Sunday, then on which day will they meet again? - The HCF
The HCF of two numbers is 18 and their product is 12960. Their LCM will be - Multiple and remainder What is the least multiple of 7, which, when divided by each one of 6,9,15,18, gives the remainder of 4 in each case?
- Known hcf and find lcm Given that HCF (306, 657) = 9, find LCM (306, 657).
- Sport field
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Roland takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many - Tailors
Find the largest number of tailors who can share either 48m or 12m of fabric equally without a reminder?
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