120∣ 2 ..60∣ 2 ..30∣ 2 ..15∣3 ....5∣ 5 ....1∣ − − − − − − − − − − − − − 160∣ 2 ..80∣ 2 ..40∣ 2 ..20∣2 ..10∣2 ....5∣ 5 ....1∣ − − − − − − − − − − 200∣ 2 100∣ 2 ..50∣ 2 ..25∣ 5 ....5∣5 ....1∣
GCF ( 120 ; 160 ; 200 ) = 2 × 2 × 2 × 5 = 40
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60,120
Factors of 160: 1, 2, 4, 5, 8, 10,16, 20, 32, 40, 80, 160
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Common Factors: 1, 2, 4, 5, 8, 10, 20, 40
Greatest Common Factor: 40
The greatest common factor (GCF) of 120, 160, and 200 is 40, which is found by determining the prime factorization of each number and identifying the common factors. The factors are calculated as follows: 2^3 for the common factor of 2 and 5^1 for the common factor of 5, resulting in GCF = 8 × 5 = 40.
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