+0  
 
0
51
4
avatar+154 

How many positive divisors do 8400 and 7560 have in common?

Creeperhissboom  Apr 24, 2018
Sort: 

4+0 Answers

 #1
avatar
+1

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 12 | 14 | 15 | 16 | 20 | 21 | 24 | 25 | 28 | 30 | 35 | 40 | 42 | 48 | 50 | 56 | 60 | 70 | 75 | 80 | 84 | 100 | 105 | 112 | 120 | 140 | 150 | 168 | 175 | 200 | 210 | 240 | 280 | 300 | 336 | 350 | 400 | 420 | 525 | 560 | 600 | 700 | 840 | 1050 | 1200 | 1400 | 1680 | 2100 | 2800 | 4200 | 8400 (60 divisors of 8400)

 

 

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 14 | 15 | 18 | 20 | 21 | 24 | 27 | 28 | 30 | 35 | 36 | 40 | 42 | 45 | 54 | 56 | 60 | 63 | 70 | 72 | 84 | 90 | 105 | 108 | 120 | 126 | 135 | 140 | 168 | 180 | 189 | 210 | 216 | 252 | 270 | 280 | 315 | 360 | 378 | 420 | 504 | 540 | 630 | 756 | 840 | 945 | 1080 | 1260 | 1512 | 1890 | 2520 | 3780 | 7560 (64 divisors of 7560)

 

OK, young person! You just have to match them by counting them. You could also factor them first and calculate the divisors:

8400 = 2^4×3×5^2×7 (8 prime factors, 4 distinct)

7560 = 2^3×3^3×5×7 (8 prime factors, 4 distinct)

Guest Apr 24, 2018
edited by Guest  Apr 24, 2018
 #2
avatar+633 
+1

I think there is an easier way.

 

You want to find the GCF of the two numbers and see how many factors that number has.

 

GCF = 2 x 3 x 5 x 7 = 210

 

210 has

 

(1+1)^4 divisors.

 

16 will be your answer,

 

I hope this helps.

 

Gavin

GYanggg  Apr 24, 2018
 #3
avatar
0

Gavin: Your method doesn't seem to match, since there are about 30 divisors that the two numbers have in common!!.

Guest Apr 24, 2018
 #4
avatar
0

Gavin's method appears to be sound, but I think he made a mistake in GCF or GCD:

 

GCD of {7,560, 8,400} =840

840 = 2^3 * 3 * 5 * 7

Then the number of divisors of 840 is =The product of the exponents of its factors + 1 for each factor:

(3+1)(1+1)(1+1)(1+1) =32 - Total divisors, which appears to agree with the actual count above.

Guest Apr 24, 2018

31 Online Users

avatar
avatar
avatar
avatar
avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy