MATHS 1 Marks Question

5600, 6000, 77622160

Yes, Guna is right. Any two prime numbers are co-prime as they do not have common factor other than 1 which means they are always co-prime. For example, 2 and 3, 5 and 7, 11 and 13.

The numbers share the common factors 3 and 7. So they are not co-prime since neither number contains all the factors of the other, neither can divide the other.

The twin primes between 1 and 100 other than 3 and 5,17 and 19 are as follows: (5, 7), (11, 13), (29, 31), (41, 43), (59, 61), (71, 73).

The seven consecutive composite numbers are: 90,91,92, 93,94, 95,96.

The valid pairs of prime numbers up to 100 that consist of the same digits are: (13, 31), (17, 71), (37, 73) and (79, 97).

Three pairs of prime numbers less than 20 whose sum is a multiple of 5 are: (2, 3), (2, 13) and (7, 13).

23 and 37 have no divisors other than 1 and themselves, making them prime.

Here, multiples df 40 are 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440
Hence multiples of 40 that lie between 310 and 410 are 320, 360 and 400.

Since the last two digits of 8536 (which is 36) are divisible by 4, the original number 8536 is also divisible by 4.

The multiples of 2 between 399 and 411 are 400, 402, 404, 406, 408,and 410.

Largest 4-digit number divisible by 4 and is also palindrome- 8888
Smallest 4-digit number divisible by 4 and is also palindrome- 2112.

Total number of composite numbers from 21 to 30 is 8.
They are 21,22,24,25, 26, 27, 28, 30.

In total, there are 2 prime numbers between 21 and 30.
They are 23 and 29.

36,48,60 are both shaded and circled. These numbers are called common multiples.

2

Numbers that are multiples of both 3 and 5 are called common multiples. The smallest common multiple of 3 and 5 is 15, and other such numbers include 30, 45, 60, and so on.

19503, 19512

(ii) 19400
(iv) 125370
(v) 3000000

The sum of the digits of the given number should be divisible by 9.
For example, 2979 is divisible by 9. (i.e.,) 2+9+7+9 = 27, which is divisible by 9.

Prime factorization of 152 = 2 × 2 × 2 × 19
Prime factorization of 76 = 2 × 2 × 19
The common prime factors of 152 and 76 are 2 and 19.

Prime factorization of
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Prime factorization of 156 = 2 × 2 × 3 × 3
The common prime factor of 256 and 156 is 2.

Since two even numbers always have two common factors, 1 and 2, they can never be co-prime numbers. Thus, 40 and 78 are not co-prime numbers.

(3, 5); (4, 9); (7, 10); (20, 29); (31, 65).

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40.

2,3,5,7,11,13,17,19

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28

19,7,11,13,23,37

(i) Composite numbers between 10 and 18 are 12, 14, 15 and 16.
(ii) Composite numbers between 61 and 69 are 62, 63, 64, 65, 66 and 68.
(iii) Composite numbers between 91 and 96 are 92, 93, 94 and 95.

17 and 71, 37 and 73, 79 and 97 are the required pairs of prime numbers up to 100.

6 is a composite number as it can be divided by more than 2 numbers 1,2,3 and 6.
2. 1 is not considered as a prime number, why? Solution:Because it does not have distinct two factors
(i.e., 1 and the number itself are the same)

The multiples of 3 are 3, 6, 9, 12, 15, 18,21,v 24, 27, 30,..
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35,40,…
Therefore, the common multiples of 3 and 5 are 15, 30, 45, 60, and so on.

The factors of 6 are 1, 2, 3 and 6.
The factors of 20 are 1,2, 4, 5, 10 and 20.
Thus, the greatest common factor of 6 and 20 is 2.

The factors of 3 are 1 and 3.
The factors of 15 are 1, 3, 5 and 15.
Therefore, the greatest common factor of 3 and 15 is 3.

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21,… . Hence, the multiples of 3 are not always the multiples of 6.
As 9, 15, 21 are not multiples of 6.

Multiples of 4 are: 4, 8, 12, 16, 20 ,
Yes, the multiples of 4 are even. Since 4 is an even number, the multiples of 4 are also even.

The factors of 25 are 1, 5 and 25
The multiples of 25 are 25, 50, 75, 100, 125, 150, and so on.

(a) The first five multiples of 23 are 23,46, 69, 92, 115.
(b) The first five multiples of 40 are 40, 80, 120, 160, 200.