Given that 527= 17x 31, is there a way to check if 77 is a factor of 527 without actually dividing 527 by 77?

Question

It's about Prime numbers

Answer 1

Hi Casey!  Do you know what numbers you can multiply to get 17?  What about 31?

 

Hope this helps!

Answer 2

 

In order for 77 to be a factor of 527, the number 527 must be divisible by all of the factors of 77.

The factors of 77 are 1, 7, and 11.

Apply the rules for divisibility by 7 and by 11.

The rule for divisibility by 7 is as follows:

 

subtract the ones digit from 527; 527-7=520

divide the result by 10; 520/10=52

subtract two times the original ones digit; 52-14=38

if you get a multiple of 7, then the original number is divisible by 7

38 is not a multiple of 7 so 527 is not divisible by 7 and therefore not divisible by 77

 

273 is divisible by 7

273-3=270

270/10=27

27-6=21

21 is a multiple of 7

 

The rule for divisibility by 11 is as follows:

 

Subtract and add the digits of the number alternately from left to right.

527;   5-2+7=10

If you get a multiple of 11 the original number is divisible by 11 but 10 is not a multiple of 11 so

therefore 527 is not divisible by 11.

 

135,795 is divisible by 11

1-3+5-7+9-5=-2+5-7+9-5=3-7+9-5=-4+9-5=5-5=0

 

107,283 is divisible by 11

1-0+7-2+8-3=1+7-2+8-3=8-2+8-3=6+8-3=14-3=11

Answer 3

 Fundamental Laws of Arithmetic : Every Composite ( Non Prime) number is uniquely product of its prime factors.

 

  527 = 17 * 31  is given

 

  77 = 7 *11

 

  So these 2 numbers don't have a common prime factor, and 527 can not be divisible to 77

 

    527  = 17*31     there is no common factor to be crossed out.

    77        7 *11