When you reverse the digits of the number 14 the number increases by 27 how many other two digit numbers increase by 27 when their digits are reversed?

When you reverse the digits of the number 13 , the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

Open in App

Suggest Corrections

NUMBER SYSTEM

1. Natural Numbers: These are the numbers (1, 2, 3, etc.) that are used for counting.

2. Whole Numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers. Whole numbers are also called as Non-negative integers.

3. Prime Numbers: A natural number larger than 1 is a prime number if it does not have other divisors except for itself and 1. (The lowest prime number is 2. 2 is also the only even prime number. The lowest odd prime number is 3.)

4. Composite Numbers: It is a natural number that has at least one divisor different from unity and itself.

5. Even Numbers: An even number is an integer that can be divided by two and remain an integer or has no remainder.

6. Odd Numbers: An integer that is not an even number is an odd number.

7. If the numbers n1 and n2 are exactly divisible by the same number x, then x is a common divisor of n1 and n2. The highest of all the common divisors of n1 and n2 is called as the GCD or the HCF.

8. Co-prime numbers are any two numbers which have an HCF of 1. (Two consecutive natural numbers are always co-prime. Two consecutive odd numbers are always co-prime. Two prime numbers are always co-prime.)

9. HCF of two or more fractions is given by: HCF of numeratorsLCM of denominators

10. LCM of two or more fractions is given by: LCM of numeratorsHCF of denominators

11. LCM × HCF = Product of two numbers (n1 × n2)

12. N =paqbrc, where, p, q and r are prime factors of the number n.

(i) a, b and c are non-negative powers/exponents

(ii) Number of factors of N = (a + 1)(b + 1)(c + 1)

(iii) Number of odd factors will be all possible combinations of powers of odd numbers (excluding any power of 2)

1. Divisibility by 2 or 5: A number is divisible by 2 or 5 if the last digit is divisible by 2 or 5.

2. Divisibility by 3 (or 9): All such numbers the sum of whose digits are divisible by 3 (or 9) are divisible by 3 (or 9).

3. Divisibility by 4: A number is divisible by 4 if the last 2 digits are divisible by 4.

4. Divisibility by 6: A number is divisible by 6 if it is simultaneously divisible by 2 and 3.

5. Divisibility by 8: A number is divisible by 8 if the last 3 digits of the number are divisible by 8.

6. Divisibility by 11: A number is divisible by 11 if the difference of the sum of the digits in the odd places and the sum of the digits in the even places is either zero or is divisible by 11.

7. Divisibility by 12: All numbers divisible by 3 and 4 are divisible by 12.

8. Divisibility by 7, 11 or 13: The integer n is divisible by 7, 11 or 13 if and only if the difference of the number of its thousands and the remainder of its division by 1000 is divisible by 7, 11 or 13.

Products:

Odd × odd = odd

Odd × Even = Even

Even × Even = Even

Get M4maths app to avail expert's solution and latest selected questions.

Download m4maths app now