Question

find the gcf of the numbers 200, 350 and 500: a.25 b.50 c.75 d.150

Explanation:

Step1: Prime Factorization

Find prime factors of each number:

• \(200 = 2^3 \times 5^2\)
• \(350 = 2 \times 5^2 \times 7\)
• \(500 = 2^2 \times 5^3\)

Step2: Identify Common Factors

Take the lowest power of each common prime factor (2 and 5 here):

• For 2: lowest power is \(2^1\) (from 350)
• For 5: lowest power is \(5^2\) (from 200 or 350)

Step3: Calculate GCF

Multiply these common factors: \(2^1 \times 5^2 = 2 \times 25 = 50\)

Answer:

B. 50