ok my h.w. says factor the following + find the greatest common factor for all of the numbers below..
then it says
Greatest common factor: ______
the numbers below this are
51, 462 , 52 , 966 , 53 , 336 , 54, 378
I have no clue what its asking me to do lol
2006-07-27 04:25:52 · 11 answers · asked by Anonymous in Education & Reference ➔ Homework Help
I'm not doing it for you, I did enough of that in 6th grade...
But it means find the greatest (highest) number that goes into all of those numbers. Trial and error works.
2006-07-27 04:28:29 · answer #1 · answered by Ty 2 · 0⤊ 1⤋
What Tom had to say is right on the money (spot on for shortening the analysis). In fact the GCF of any number and a prime number is going to be 1.
However, if you also need to know the LCD (Least Common Denominator) which is something you typically do when trying to combine fractions with those numbers in the list as the denominators here is some more help. These two topics are both related by factoring:
51 = 3*17
462 = 2*3*7*11
52 = 2*2*13
966 = 2*3*7*23
53 = 53 (prime number)
336 = 2*2*2*2*3*7
54 = 2*3*3*3
378 = 2*3*3*3*7
So now we combine all the unique factors to get:
2*3*7*11*13*17*23*53 = 124462338
Hope you don't need to add fractions with that as the common denominator
2006-07-27 05:09:57 · answer #2 · answered by Will 4 · 0⤊ 0⤋
Ok... First you need to understand what the Greatest Common Factor (GCF) means. The GCF is the largest number that can evenly divide into EACH of your numbers given. You should first start by breaking down each number into its Prime Factors...
Instead of your numbers, let's work with 8 and 30:
8 = 2*2*2, 30 = 2*3*5; so you can readily see that the common factor is 2 (only one 2 in each one matches with the factors in the other set)
take 8 and 60: 8 = 2*2*2, 60 = 2*2*3*5; so you can see that there are two 2's in each set of factors... so your gcf is 2*2 or 4... none of the other numbers are common.
Now for your numbers: I would arrange the numbers you have into numerical order so it is easier to work with and see any trends:
51, 52, 53, 54, 336, 378, 462, 966
then take them one at a time and factor them out:
take 51 and break it down in to Prime Factors and you get:
(3,17)
take 52 and break it down into Prime Factors and you get:
(2,2,13)
Ok.. we'll stop right here... take a look at the prime factors for 51 and 52... there are NONE in common... so there is no prime number that will divide evenly into both 51 and 52... so, your ONLY common factor for these two numbers is 1.
Since 1 is the only common factor... it is your Greatest Common Factor.
2006-07-27 04:51:29 · answer #3 · answered by ♥Tom♥ 6 · 0⤊ 0⤋
You're looking for the highest number you can find that will go into all of those numbers. A number they can all be divided by. For example, if you had 4, 6, 8 the common highest factor is 2. They can all be divided by 2.
Here's a couple of hints to get you started.
Since there are odd numbers in this set, it's not going to be an even number, since any an odd number multiplied by an even number is even and an even number multiplied by an even number is even.
Also, another tip.. if you add up the digits and the sum is divisible by 3, then the number will be too. Such as 33. 3+3=6. 6 is divisible by 3, so 33 will be too!
2006-07-27 04:32:57 · answer #4 · answered by butireallyam_nikkijd 3 · 0⤊ 0⤋
You have to do factor trees for each number, and yes, the GCF = 1. By the way 51 = 3 x 17, and 53 is prime.
2006-07-27 04:32:31 · answer #5 · answered by Speedy 3 · 0⤊ 0⤋
51 is a prime number (not divisible by anything but itself and one)
462=231*2 and 231 is not divisible by 51
no other number is divisible by 51
52=26*2=13*4 but none of the other numbers are divisible by 13
and so on...
my guess is that 1 is the greatest common factor
2006-07-27 04:37:43 · answer #6 · answered by Magnus L 1 · 0⤊ 0⤋
First find the factors if these numbers. for example for 51 = 51 and 1. something like that. after you find the factors for each, look at the numbers, then choose the greatest common number in them. I don't think the instructions are that clear.
2006-07-27 04:31:46 · answer #7 · answered by chalyde 2 · 0⤊ 0⤋
It is asking you to find the largest number that goes into all of the numbers listed. The number 51 makes it real easy; especially since 53 is included on your list.
2006-07-27 04:31:57 · answer #8 · answered by Caffeinated 4 · 0⤊ 0⤋
51 = 17, 3 ------------- 462 = 154, 3
52 = 14, 3 ------------- 966 = 69,14
53 = Prime
54 = 27, 2 ---------------378 = 27, 14
2006-07-27 04:38:31 · answer #9 · answered by Chappy 3 · 0⤊ 0⤋
The answer is 1
It is the greatest (and only) number that will divide evenly into all of the numbers in that list.
2006-07-27 04:30:15 · answer #10 · answered by jimvalentinojr 6 · 0⤊ 0⤋