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describe strategies for finding factors or multiples of a number

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3 Answers

let me add to the already given answers
 
divisibility by 7: there are three steps-step 1) subtract the ones digit from the number
                                                       step 2) divide the result by 10
                                                       step 3) subtract 2 times the original ones digit from the second result
                                                       if you get a multiple of 7 (or 0, which is a multiple of all numbers), then the original number is divisible by 7
examples: is 161 divisible by 7 ?
161-1=160
160/10=16
16-2*1=16-2=14, a multiple of 7
 
is 126 divisible by 7 ?
126-6=120
120/10=12
12-2*6=12-12=0, a multiple of 7
 
is 952 divisible by 7 ?
952-2=950
950/10=95
95-2*2=95-4=91, a multiple of 7 (7*13=91)
if you did not know that 91 was a multiple of 7, simply repeat the steps with 91
91-1=90
90/10=9
9-2*1=9-2=7, obviously a multiple of 7
 
divisibility by 8: a number is divisible by 8 if the number formed by the three right-most digits is divisible by 8(the number in question has to be at least 4 digits in length in order for the rule to be useful)
examples: is 1536 divisible by 8 ?
                check to see if 536 is divisible by 8
                536 is divisible by 8 (536/8=67)
 
                is 502,872 divisible by 8 ?
                check to see if 872 is divisible by 8
                872 is divisible by 8 (872/8=109)
 
divisibility by 11: take the digits that form the number and subtract and then add them one at a time from left to right; if you get 0 or a multiple of 11 then the number is divisible by 11 
examples: 132        1-3+2=0
                13,574    1-3+5-7+4=0
                75,845    7-5+8-4+5=11
 
also, you can make up your own divisibility rules
a number is divisible by 12 if it is divisible by both 3 and 4
a number is divisible by 14 if it is divisible by both 2 and 7
a number is divisible by 15 if it is divisible by both 3 and 5
the numbers  must not have any common factors except 1 (3 and 4, 2 and 7)
 
 
 
Hey Brian! Finding factors and multiples revolves around the divisibility rules for the numbers 2, 3, 4, 5, 6, 9, & 10. Here they are:
 
2: If the last digit of your number is even (divisible by 2), then the entire number is divisible by 2.
3: Add up all of the digits of your number, and if that sum is divisible by 3, then the entire number is divisible by 3.
4: If the last TWO digits of your number is divisible by 4, then the entire number is divisible by 4.
5: If the last digit of your number is a "5" or "0", then the entire number is divisible by 5.
6: If you have determined that your number is divisible by 2 AND 3, then your number is also divisible by 6.
9: Add up all of the digits of your number, and if that sum is divisible by 9, then the entire number is divisible by 9.
10: If the last digit of your number is a "0", then your number is divisible by 10.
 
These are the most common factors and the easiest to determine, so they are also the fastest. Use these rules to test large numbers to see if they can be factored. If they can be factored by a number, then it is a MULTIPLE of that number. You can also create multiples by using the rules. For instance, if you want a large multiple of 3, then create a number where the digits add up to a multiple of 3 (4,281 adds up to 15, which can be divided by 3).
 
I hope this helps you!
Finding a factor is finding two numbers that multiply together to give that number. Or simply finding what numbers divide evenly into that number.
The factors of 24 are found by asking yourself what times what gives me 24?
1 x 24
2 x 12
3 x 8
4 x 6
 
So the factors of 24 are 1,2,3,4,6,8,12, and 24. The is a finite number of factors.
 
Finding multiples of a number is simply "counting by" that number. The multiples of 2 are 2,4,6,8,10,12,14,...
The multiples of 5 are 5,10,15,20,25,30,...
As you can see there are an infinite number of multiples of a number