Explanation

Step 1: Find the prime factors of each number

255 = 3 × 5 × 17

345 = 3 × 5 × 23

495 = 3² × 5 × 11

Step 2: Identify the common factors

The common prime factors are 3 and 5.

Step 3: Calculate the HCF

HCF = 3 × 5 = 15

Explanation

To find the LCM, break down the numbers into their prime factors:

12 = 2² * 3

15 = 3 * 5

20 = 2² * 5

30 = 2 * 3 * 5

Step 1: Identify the highest powers of prime factors

The highest power of 2 is 2² (from 12 and 20).

The highest power of 3 is 3 (from 12, 15, and 30).

The highest power of 5 is 5 (from 15, 20, and 30).

Step 2: Calculate the LCM

LCM = 2² * 3 * 5

= 4 * 3 * 5

= 60

Explanation

if A=1, B=3, C=5, and so on, the number 3, 9, and 7 stands for BED

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Explanation

In large numbers, commas are placed after every three digits starting from the right.

For example, 1,000 and 10,000,000 have commas after every three digits.

Explanation

The numbers whose squares end with 6 are those ending in 4 or 6.

Let's find the first two perfect squares that end with 6:

1. 4^2 = 16

2. 6^2 = 36

The difference between these two perfect squares is:

36 - 16 = 20

Explanation

To find the greatest number that exactly divides 145, 360, and 578, we need to find their greatest common divisor (GCD or HCF).

Let's find the factors:

145 = 5 × 29

360 = 2^3 × 3^2 × 5

578 = 2 × 17 × 17

The only common factor is 1.

Explanation

Even numbers end in 0, 2, 4, 6, or 8.

4869 ends in 9, so it is not an even number.

Explanation

Zero is a whole number.

It belongs to the set of whole numbers (0, 1, 2, 3, ...).

Natural numbers start from 1 (1, 2, 3, ...).

Explanation

Three consecutive odd intergers can be identified as x, x+2, x+4 so,

x + (x+2) + (x+4) = 105

3x + 6 = 105

3x = 99

x = 33 

Explanation

To multiply fractions, multiply the numerators and denominators:

(5 × 7) / (14 × 10) = 35 / 140 = 1/4