Given two diamonds with same shape but different sizes.
The side given of one diamond = 10 units.
And the corresponding side of the other diamond = 24 units.
To find the scale factor of them, we need to find the ratio of the sides.
So here scale factor =
= 
Now we have to simplify the fraction. We can simplify it by dividing the numerator and denominator by a common factor of it.
The common factor of 10 and 24 is 2. If we divide 10 by 2, we will get 5 and if we divide 24 by 2, we will get 12.
So we will get,

We have got the required answer.
The scale factor is
.