Question

A block is cut into equal units.

of 10 g, 20g and 35g.Use prime
factorization method to find the
smallest possible mass of the block
from which pieces can be cut​

Answer 1

140 g

Explanation:

Note that

• 
  `10=\underline{2}\cdot \mathbf{5};`
• 
  `20=\underline{2}\cdot 2\cdot \mathbf{5};`
• 
  `35=\mathbf{5}\cdot 7`

As you can see 5 is the common factor for all three numbers and 2 is the common factor only for the first two numbers. So, the greatest common factor

`GCF(10,20,35)=5\cdot 2\cdot 2\cdot 7=140\ g.`

The smallest mass of the block should be 140 g (it can be cut into 14 pieces of 10 g weight, 7 pieces of 20 g weight or 4 pieces of 35 g weight).