How can you use prime factorization to determine if 856 is evenly divisible by 7?

Question

Roman Alvarez · Accepted Answer

#856# is not evenly divisible by #7#

You can reduce the size of the problem if you can separate out other prime factors.

#color(white)(00000)856# #color(white)(00000)"/"color(white)(0)"\"# #color(white)(0000)2color(white)(00)428# #color(white)(0000000)"/"color(white)(0)"\"# #color(white)(000000)2color(white)(00)214# #color(white)(000000000)"/"color(white)(0)"\"# #color(white)(00000000)2color(white)(00)107#

If we knew that #107# is prime then we would be done.

The next factor to try would be #7#, which is the one we're wanting to test anyway.

I'm not sure this factorisation has helped us much, but let us at least split it down to make the arithmetic a little easier:

#107 / 7 = (70+35+2) / 7 = 70/7+35/7+2/7 = 10+5+2/7 = 15 2/7#

So #107# is not divisible by #7# and neither is #856#.

Skylar Adams · Answer

undefined To determine if 856 is evenly divisible by 7, we can use the divisibility rule for 7, which involves repeatedly subtracting multiples of 7 until a number that is easily divisible by 7 is obtained. Alternatively, we can use prime factorization. If the prime factorization of a number includes the prime factor of 7, then the number is divisible by 7.