Renson has three pieces of wood of length 91 m, 112 m, and 49 m. If he wants to cut the wood into equal planks, what is the greatest possible length (in m) of each plank?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 7.
91 is divisible by 7, so we divide:
⇒ 91 ÷ 7 = 13
⇒ 91 = 7 × 13
112 is divisible by 2,
⇒ 112 × 2 = 56
⇒ 7
The prime factorization of 112 is:
⇒ 112 = 24 × 7
49 is divisible by 7,
⇒ 49 ÷ 7 = 7
⇒ 49 = 72
The only common prime factor is 7, and the lowest power of 7 that appears in all three factorizations is ( 7 ).