Find out Greatest Common Divisor(GCD)
GCD or GCM: Highest Common Factor also called as Greatest Common Measure(GCM) or Greatest Common Divisor(GCD). GCD of two or more numbers is the greatest number that can exactly divide each one of the number.
Example: Say we have 2 numbers 4,8. The numbers that can divide 4 and 8 are 2,4. Here 4 is the highest number that can exactly divide both 4 and 8 , so 4 is the HCF of 4,8.
GCD can be calculated by any of the following methods,
Factorization Method:
Express each one of the numbers as product of prime factors.
The product of least powers of common prime factors gives GCD.
Example:
Greatest Common Measure of 36, 90, 72.
Step1: Express the numbers as product of prime factors. 36 = 22 × 32 90 = 2 × 5 × 32 72 = 23 × 32
Step2: Take the prime numbers with least power and is present in all sets.
2 and 3 are the prime number common to all given numbers. The least power of 2 in the set is - 2 The least power of 3 in the set is - 32
Step3: Product of the numbers taken. 32 × 2 = 9 × 2 = 18 So 18 is the GCD(Greatest Common Divisor) of the numbers.
Division Method:
Two find the GCD of two given numbers, divide the largest by the small number, then divide the dividend by the remainder. Repeat this until remainder is 0. The last dividend is the HCF of the two numbers.
Example: GCD of 27 & 36 Step1: Divide 36/27 -> remainder = 9 Step2: Divide dividend by remainder 27/9 -> remainder = 0 So the GCD(greatest common Divisor) of 27 and 36 is 9
For 3 numbers, calculate the GCD or greatest common measure(GCM) of 2 numbers, then GCD of the result with 3rd number.
LCM: LCM of two or more numbers is the least number that is exactly divisible by each one of the given numbers.
Least Commmon Factor(LCF) can be calculated by any of the following method,
Factorization Method:
Express each one of the numbers as product of prime factors.
The product of highest powers of all prime factors gives LCF.
Example:
Least Common Multiple or Factor of 36, 90, 72.
Step1: Express the numbers as product of prime factors. 36 = 22 × 32 90 = 2 × 5 × 32 72 = 23 × 32
Step2: Take the prime numbers with highest power for all prime numbers.
2, 3,5 are the prime number identified. The highest power of 2 in the set is - 23 The highest power of 3 in the set is - 32 The highest power of 5 in the set is - 5
Step3: Product of the numbers taken. 32 × 5 × 23 = 9 × 5 × 8 = 360 So 360 is the LCM (Least Common Multiple) of the numbers.
1. 1 x 8 + 1 = 9 12 x 8 + 2 =98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 98765 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 +8 = 98765432 123456789 x 8 + 9 = 987654321
2. 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 + 10 = 1111111111
3. 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888
4. 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321
5. 12345679 x 09 = 111111111 12345679 x 18 = 222222222 12345679 x 27 = 333333333 12345679 x 36 = 444444444 12345679 x 45 = 555555555 12345679 x 54 = 666666666 12345679 x 63 = 777777777 12345679 x 72 = 888888888 12345679 x 81 = 999999999
6. 9 x 9 = 81 99 x 99 = 9801 999 x 999 = 998001 9999 x 9999 = 99980001 99999 x 99999 = 9999800001 999999 x 999999 = 999998000001 9999999 x 9999999 = 99999980000001 99999999 x 99999999 = 999999980000001; 999999999 x 999999999 = 999999998000000001;
7. 6 x 7 = 42 66 x 67 = 4422 666 x 667 = 444222 6666 x 6667 = 44442222 66666 x 66667 = 4444422222 666666 x 666667 = 444444222222 6666666 x 6666667 = 44444442222222 66666666 x 66666667 = 4444444422222222 666666666 x 666666667 = 444444444222222222
2. 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 + 10 = 1111111111
3. 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888
4. 1 x 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321
5. 12345679 x 09 = 111111111 12345679 x 18 = 222222222 12345679 x 27 = 333333333 12345679 x 36 = 444444444 12345679 x 45 = 555555555 12345679 x 54 = 666666666 12345679 x 63 = 777777777 12345679 x 72 = 888888888 12345679 x 81 = 999999999
6. 9 x 9 = 81 99 x 99 = 9801 999 x 999 = 998001 9999 x 9999 = 99980001 99999 x 99999 = 9999800001 999999 x 999999 = 999998000001 9999999 x 9999999 = 99999980000001 99999999 x 99999999 = 999999980000001; 999999999 x 999999999 = 999999998000000001;
7. 6 x 7 = 42 66 x 67 = 4422 666 x 667 = 444222 6666 x 6667 = 44442222 66666 x 66667 = 4444422222 666666 x 666667 = 444444222222 6666666 x 6666667 = 44444442222222 66666666 x 66666667 = 4444444422222222 666666666 x 666666667 = 444444444222222222
1.multiply the 1st digit of your age by 5. (example:age 25,so 2*5=10)
2.add 3 with the result. (10+3=13)
3.double the answer. (13*2=26)
4.add the second digit of your age with the result. (26+5=31)
5.subtract 6 from it. (31-6=25)
this result is your age....
2.add 3 with the result. (10+3=13)
3.double the answer. (13*2=26)
4.add the second digit of your age with the result. (26+5=31)
5.subtract 6 from it. (31-6=25)
this result is your age....
1.think of 2 single digit number. (example: 5,3)
2.take any one of the number among them and double it. (3*2=6)
3.Add 5 with the result. (6+5=11)
4.multiply the result with 5. (11*5=55)
5.add the second number to the answer. (55+5=60)
6.subtract the answer with 4. (60-4=56)
7.subtract the answer again with 21. ( 56-21=35)
8.the answer would be the 2 single digit number.
now make fun with your friends...:D
2.take any one of the number among them and double it. (3*2=6)
3.Add 5 with the result. (6+5=11)
4.multiply the result with 5. (11*5=55)
5.add the second number to the answer. (55+5=60)
6.subtract the answer with 4. (60-4=56)
7.subtract the answer again with 21. ( 56-21=35)
8.the answer would be the 2 single digit number.
now make fun with your friends...:D
1.Think of a number below 10 example:(5)
2.double the number (5*2=10)
3.add 6 with the getting result (10+6=16)
4.half the number (16/2=8)
5.take away the number you thought from the answer. (8-5=3)
6.answer is 3.
for all numbers below 10,the result would be 3.now you can show mathematics magic.
2.double the number (5*2=10)
3.add 6 with the getting result (10+6=16)
4.half the number (16/2=8)
5.take away the number you thought from the answer. (8-5=3)
6.answer is 3.
for all numbers below 10,the result would be 3.now you can show mathematics magic.
its osssssaaaaaaam
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