CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A number a has 7 as its smallest prime factor, and another number b has 3 as its smallest prime factor. What is the smallest prime factor of the number a+b?


A

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

7

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

2


Since 7 is the smallest prime factor of a, it is clear that 2 is not a factor of a. Thus, a is an odd number, i.e. a=2n+1 for some n.


Similarly, when 3 is the smallest prime factor of b, 2 cannot be a factor of b and thus b is also odd.i.e., b=2m+1 for some m.


Hence we have a+b=(2n+1)+(2m+1)=2(n+m+1)=2k ( taking 2 common and assuming k=n+m+1.)


We can thus see that 2 is a factor of a+b, and hence 2 is the smallest prime factor of a+b.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Factors of a Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon