Prime Time MATHS - Prime Time

A number is divisible by 5, if it has

The largest number, which always divides the sum of any pair of consecutive odd numbers is

Which number is divisible by 8?

Which pair of number is coprime?

Which of the following numbers is not a composite number?

Assertion (A) The number 1 is considered a prime number.
Reason (R) A prime number must have exactly two distinct factors.

Assertion (A) The common factors of two numbers can never be greater than the smaller number.
Reason (R) Factors are numbers that divide another number completely.

Assertion (A) Tne number 9 and 25 are coprime. Reason (R) A number is said to be prime-, if it has only two factors 1 and the number itself.

A number is divisible by 4 if the last three digits form a number that is divisible by 4.

All prime numbers are coprime with each other.

Composite numbers have more than two factors.

All even numbers are prime numbers.

The common factors of 6 and 9 are 1 and 3.

If two numbers have’no common factors other than 1, they are said to be _______________ .

Numbers having more than two factors are called _______________ numbers.

The smallest prime number between 80 and 90 is _______________

A number for which the sum of all its factors is equal to twice the number is called a _______________ number.

15 is a multiple of _______________ and _______________ .

Which of the following numbers are divisible by all of 2, 4, 5, 8 and 10: 572, 2352, 5600, 6000, 77622160?

Guna says, “Any two prime numbers are co-prime”. Is he right?

The first number has prime factorization 2 × 3 × 7 and the second number has prime factorization 3 × 7 × 11. Are they co-prime? Does one of them divide the other?

Twin primes are pairs of primes having a difference of 2. For example, 3 and 5 are twin primes. So are 17 and 19. Find the other twin primes between l and 100.

Find seven consecutive composite numbers between 1 and 100.

Write two numbers whose product is 10000. The two numbers should not have 0 as the units digit.

The teacher asked if 14560 is divisible by all of 2, 4, 5, 8 and 10. Guna checked for divisibility of 14560 by only two of these numbers and then declared that it was also divisible by all of them. What could those two numbers be?

Explore and find out if each statement is always true, sometimes true or never true. You can give e×amples to support your reasoning.
(a) Sum of two even numbers gives a multiple of 4.
(b) Sum of two odd numbers gives a multiple of 4.

2024 is a leap year (as February has 29 days). Leap years occur in the years that are multiples of 4, e×cept for those years that are evenly divisible by 100 but not 400.
(a) From the year you were born till now, which years were leap years?
(b) From the year 2024 till 2099, how many leap years are there?

What is the smallest number whose prime factorization has:
(a) three different prime numbers?
(b) four different prime numbers?

Find the remainders obtained when each of the following numbers are divided by
(i) 10
(ii) 5
(iii) 2.
78, 99, 173, 572, 980, 1111, 2345

Is the first number divisible by the second? Use prime factorization.
(a) 225 and 27
(b) 96 and 24
(c) 343 and 17
(d) 999 and 99

Are the following pairs of numbers co-prime? Guess first and then use prime factorization to verify your answer.
(a) 30 and 45
(b) 57 and 85
(c) 121 and 1331
(d) 343 and 216

Find the prime factorization of these numbers without multiplying first.
(a) 56 × 25
(b) 108 × 75
(c) 1000 × 81

Find the smallest number that is a multiple of all the numbers from 1 to 10.

Identify whether each statement is true or false. Explain.
(a) There is no prime number whose units digit is 4.
(b) A product of primes can also be prime.
(c) Prime numbers do not have any factors.
(d) All even numbers are composite numbers.
(e) 2 is a prime and so is the next number, 3. For every other prime, the next number is composite.

Find the prime factorizations of the following numbers: 64, 104, 105, 243, 320, 141, 1728, 729, 1024, 1331, 1000.

Look at the list of primes till 106. What is the smallest difference between two successive primes? What is the largest difference?