Shortcuts to find HCF and LCM
In the view of competition, finding problems on HCF and LCM needs you to be much actuated. Keeping an eye on each factor and making out the major dissimilarity between two concepts is really a hard over and above puzzling task. So friends! Let’s clear both the concepts and make them on your tips to perform best in your examinations. Before going further take a look onTest of Divisibility
:Divisibility by 2 or 5: A number is divisible by 2 or 5 if the unit digit is divisible by 2 or 5.
Divisibility by 3: A number is divisible by 3 if the sum of its digit is divisible by 3. (For example 695421, here sum of all digits=27 which is divisible by 3)
Divisibility by 4: A number is divisible by 4 if the last two digits are divisible by 4(For example 6879376 is divisible by 4 as last digits 76 is divisible by 4)
Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.(For example 24 divisible by both 2 and 3 both)
Divisibility by 8: A number is divisible by 8 if the number formed by hundred’s, ten’s and unit’s digit of number is divisible by 8.(For example 16789352 is divisible by 8 as number formed by last three digit i.e. 352 is dividable by 8)
Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.(For example 246591 is divisible by 9 as sum of its digits is 27 divisible by 9)
Divisibility by 10: A number is divisible by 10 only when unit digit is 0. (For example 3200 is completely divisible by 3)
Divisibility by 11:A number is divisible by 11 if the difference between the sun of digit at odd places and at even places is either 0 or divisible by 11.( For example 29435417 is divisible by 11 as (7+4+3+9)-(1+5+4+2)=23-12=11 is divisible by 11)
Divisibility by 7,11,13: A number is divisible by 7,11 and 13 if and only if the difference of its thousand and reminder is divisible by 7,11 and 13 ( For example 473312 is divisible by7 since 473-312=161 is divisible by 7)
Divisibility by 12: All the numbers divisible by 3 and 4 both are divisible by 12.
HCF or GCM or GCD
Highest common Factor or Greatest Common Multiple or Greatest Common Divisor of two numbers is the greatest number that divides each of them exactly.Methods to find HCF:
Method1 :Finding highest Factor
Take an example:Find the HCF of 8, 12, and 24Step1: Split number into their individual factors as:Step2: Find the common factor among factors of three numbers.Step3: 4 is highest common factor among factors of three numbers. Hence the HCF of 8, 12 and 24 is 4.Method 2 :Factorization:
Take the same example:Step1: Find the multiples of given number:8= 2x2x212=2x2x324=2x2x2x3 Step2: Then express the given number as prime factors8= 2x2x2 or you can write 23×30 12=2x2x3 or 22×31 24=2x2x2x3 or 23×31 Step3: Find the product of least power of common prime factors 22×30 = 4 is the least power and is the HCF of 8, 12, and 24 Method 3 :Division Method
Take the same example:Step1: Divide larger number by smaller number and then divide the divisor by remainder:Step2: Repeat the process till 0 is obtained as remainder.Step3: The last divisor is required HCF i.e. 4
Take an example:Find the LCM of 16, 24, 36 and 54Step1: Divide the numbers till 1 is obtained:Step2: Find the LCM by multiplying the divisors:LCM= 2x2x2x3x3x3x2=432*****************************************NOTE******************************************HCF and LCM Of fractions:HCF= HCF of Numerator/LCM of Denominator<//li>
LCM= LCM of Numerator/HCF of Denominator
IMPORTANT FACTS:Product of two number= Product of HCF X LCM
If HCF of x & y is A then HCF of x, (x+y) is also G.
If HCF of x & y is A then HCF of x, (x-y) is also G.
If HCF of x & y is A then HCF of (x-y), (x+y) is also G.
Google got new stunning logo
Following a recent shocking update from Google about his new move to come under “Alphabet”, Company has now decided to recreate or in other words ‘Refine’ its Logo. (bit.ly/1EvU49a)
When you will visit the Google page, a hand rubbing and rewriting Google Doodle in the new sans-serif typeface containing colored crayon is really interesting to look at. In the end, hand tilted the “e” little bit upwards. Besides this, the blue letter ‘g’ is capitalized to ‘G’ and presented in the colored form.
Journey of Logo designs:
Getting into the history, Google has resigned its logo several times.
In 1998: Sergey Brin designed a computerized version of Google logo by using the GIMP (Graphical program).
In 1999: Exclamation mark and color of G (Green to blue) has been supplemented to logo as to give a new refined look.
In 2010: Company recreated the logo and designed in Catull typeface removing exclamation mark.
In 2013: Till 2013, the logo reconstructed to reduce the distance of the shadow projection as well as modify Google’s second ‘o’ with the distinct yellow color.
Till 2015: Logo revamped to flat letters along with the remotion of shadows.
Finally revealed in September 2015: The new sans-serif typeface logo renovated
Shaping its future
With the new revised logo, Company is all set to bang up its new looks, features and products in the market.In the company last blog (bit.ly/1JvGik1) , Google said, while highlighting all about the logo.“Aims to make Google more accessible and useful to our users” Google considering this new footstep as giving an outstanding turn to the company, shaping its future with infallible image as said in the blog…
Short term Loans Long term Loans Liabilities: Liabilities are the obligations in the form of debt or payments you owe to some other company. Every year company balance sheets cover liability as legal debt or an accrual that tells approximately how much you have to pay. It accepts Deposits like:Demand Deposit
Banks usually offers the facility of opening various types of accounts in which deposits can deposit their money and without at the time of financial needs. Depending on the nature of accounts money can be withdrawn.There are two Types of deposit:
Demand Deposits are payable on account holder’s financial requirement. The money always stays in saving accounts such as medium of exchange. Via Cheques, ownership of demand deposit can be shifted from one person to another. It has no fixed term of maturity. There are two types of demand deposits:
Current Account:A current accounts is also called demand deposits because account holder can withdraw his/her money when required and bank is always obliged to pay the money on demand.
Saving Account: This account is meant for people who have limited necessities and intended to save their money with less withdrawal.
Pay in Slip:Pay-in-slip are printed forms with perforated foil used for deposition cash or cheques . IT usually contains name of account holder, account number, amount deposit and signature of person depositing it.
Current Account Saving account (CASA) Deposits. As name suggest it is mixed form of both current and saving account. Through CASA, various services like salary accounts to company, encouraging merchants to open current accounts etc are available. CASA deposits are low interest deposits compare to other deposits but The Bank with high CASA ratio are more than low CASA ratios.
In Time deposits, money is saved for the fixed time period whereas payable on or after maturity of fixed period. No more cheque facility available during the deposit term. Money only paid on maturity at a particular time. Three types of Time Deposits are:
Fixed Deposits: Some amount of money is deposited for a fixed time period at fixed rate of interest. Time period for fixed deposits starts from 7 days to 10 years. After the specific time, the depositor can withdraw the money or can renew the FD for further specified time.
Re-investment Deposits: In recurring deposits, the amount is compounded quarterly and procedure contains the payment on the day of its maturity along with deposit’s principal amount. In FD amount in saving deposit account outside a fixed limit is changed into the term deposit.
Recurring Deposits: FD amount is deposited regular interval for fixed term and the repayment of principal and accumulated interest is made at the end of the term. These deposits are usually targeted the repayment of principal and accumulated interest is made at the end of the term. These deposits are usually targeted at person who are salaried and receive other regular income. The time period for RD starts from 6 months to 120 months.