how do you find the greatest common of. 16 and 42; 8 and 18; 77 and 15
"greatest common" what?
greatest common factor?
16 and 42:
ask yourself, what is the largest number that divides exactly into both 16 and 42.
Isn't it 2?
Method:
16 = 2*2*2*2
42=2*3*7
which numbers or group of numbers are common, I see only one 2 which is common
77 = 7*11
15 = 3*5
there are no common factors.
another exampe : 48 and 120
48 = 2*2*2*2*3
120 = 2*2*2*3*5
the highest(greatest) common factor is
2*2*2*3 or 24
check it, does 24 divide into each one?
Is there a larger number?
The greatest common factor is the largest number that goes evenly into both numbers.
16 is divisible by 1, 2, 4, 8, 16
42 is divisible by 1, 2, 3, 6, 7, 14, 21, 42.
The greatest common factor of 16 and 42 is 2 because it's the largest divisor of both numbers.
If you post your answers for the other two sets of numbers, we'll be glad to check them.
This site also explains GCF.
http://amby.com/educate/math/2-1_GCF.html
To find the greatest common divisor (GCD) of two numbers, you can use a method called Euclid's algorithm. Here's how you can find the GCD of each pair of numbers you mentioned:
1. GCD of 16 and 42:
- Divide the larger number (42) by the smaller number (16): 42 ÷ 16 = 2 with a remainder of 10.
- Now, divide the smaller number (16) by the remainder (10): 16 ÷ 10 = 1 with a remainder of 6.
- Repeat the process by dividing the previous remainder (10) by the new remainder (6): 10 ÷ 6 = 1 with a remainder of 4.
- Continue the process by dividing the previous remainder (6) by the new remainder (4): 6 ÷ 4 = 1 with a remainder of 2.
- Finally, divide the previous remainder (4) by the new remainder (2): 4 ÷ 2 = 2 with no remainder.
- The GCD of 16 and 42 is the last non-zero remainder, which is 2.
2. GCD of 8 and 18:
- Divide the larger number (18) by the smaller number (8): 18 ÷ 8 = 2 with a remainder of 2.
- Now, divide the smaller number (8) by the remainder (2): 8 ÷ 2 = 4 with no remainder.
- The GCD of 8 and 18 is the last non-zero remainder, which is 2.
3. GCD of 77 and 15:
- Divide the larger number (77) by the smaller number (15): 77 ÷ 15 = 5 with a remainder of 2.
- Now, divide the smaller number (15) by the remainder (2): 15 ÷ 2 = 7 with a remainder of 1.
- Finally, divide the previous remainder (2) by the new remainder (1): 2 ÷ 1 = 2 with no remainder.
- The GCD of 77 and 15 is the last non-zero remainder, which is 1.
Therefore, the greatest common divisors are:
- GCD of 16 and 42: 2
- GCD of 8 and 18: 2
- GCD of 77 and 15: 1