What are significant figures?

Significant figures are important or interesting figures. The first non – zero digit of the number is the significant figure of that number. Significant figures examples are as follows: -
• Number 34,566 has five significant figures and the first significant figure is 3 and the second significant figure is 4.
• Number 0.0005487 has four significant figures and the first significant figure is 5 and the second significant figure is 4.
• Number 3000 has one significant figure and that is 1.
• Number 1500.00 has six significant figures and the first significant figure is 1 and the second significant figure is 5.
• Number 350. Has three significant figures and 3 is the first significant figure and 5 is the second significant figure.
• Number 350 has two significant figures and 3 is the first significant figure and 5 is the second significant figure.
Rules for Significant figures
Following are the significant figure rules: -
1. Zeros in between a number are always significant. For example, both 3406 and  30.07 have four significant figures
2. Zeros that only set the decimal points are not significant. For example, 36000 have only two significant figures.
3. Zeros that are not needed to hold the decimal point are significant. For example, 36.00 have four significant figures.
Properties of Significant figures
Addition and Subtraction with Significant figures: When significant figures are added or subtracted, the answer can contain no more decimal places than the least accurate measurement.
For example: -
140.0 + 0.608 = 140.6
Multiplication and Division of Significant figures: When significant figures are multiplied or divided, the answer can contain no more decimal places than the least accurate measurement.
For example: -
3.531/ 553.6 = 0.006378
Rounding off Significant figures: When any solutions contain so many significant figures, it can be rounded off.

For example: -
If digit is smaller than 5 then the digit remains unchanged, such as 2.43 can be rounded off to 2.4
If the digit is greater than 5 or then we should drop that digit and add one to the preceding digit, such as 2.47 can be rounded off to 2.5

Greatest Common Factor

What is GCF or What is Greatest Common Factor? 
GCF is the greatest of the common factors of the numbers.
By the definition of GCF, Greatest Common Factor is the largest number that factors into two or more greater numbers.
For instance, the GCF of 25 and 30 is 5, as 5 is the largest number that divides 25 and 30 evenly
Let us learn how to find GCF or how to find Greatest Common Factor:
First let us understand what factors are.
Factors are the numbers when multiplied together give another number

For instance, 4 x 6 = 24
4 and 6 are called the factors of 24
Now, let us understand what common factors are.
When we list out all the factors of given two or more numbers, the common factors are those found in both the lists.

For instance, factors of 18 and 24
18 = 1, 2, 3, 6, 9, 18
24 = 1, 2, 3, 4, 6, 8, 12, 24
The common factors from the above list are 1, 2, 3, and 6 as they appear in both the lists
To find the GCF of given two or more numbers, we follow a set of steps:
1. List out all the factors of the given numbers
2. From the list of factors, we need to list out all the factors that are common
3. The greatest of the common factors is the required GCF of the given numbers

Example: Find the GCF of 56,  84 and 112
Solution: Factors of,
56 = 1,2, 4,7, 8,14,28,56
       84= 1,2, 3,4,6,7, 12, 14,21,28,42,84
          112= 1,2,4,7, 8,14,16,28,56,112
Common factors from the above list are:
 1, 2, 4, 7, 14 and 28
Highest of the common factors is 28
So, the GCF of 56, 84 and 112 is 28

Greatest Common Divisor:
The Greatest Common Divisor or GCD of two numbers is in other words called Greatest common factor (GCF), which is the largest number that is a divisor (factor) of both the numbers.

Example of GCD

For instance, the largest number that divides both 24 and 18 is 6.