What is the greatest common factor of 18 and 130?
Answer (3)
18∣2 . 9∣3 . 3∣3 . 1∣ 18 = 2 × 3 × 3 − − − − − − − − − − − − − − 130∣2 . 65∣5 . 13∣13 . 1∣ 130 = 2 × 5 × 13 − − − − − − − − − − − − − − − GCF ( 18 ; 130 ) = 2
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 18 and 130, you can list the factors of each number and then find the highest number that appears on both lists. However, in this case, since 130 is an even number and 18 is also even, we know that 2 is a common factor. Given that 130 is not divisible by 3 or 9, which are factors of 18, and 18 does not contain the prime factor 5 that is present in 130, we can determine that 2 is indeed the greatest common factor of 18 and 130.
The greatest common factor (GCF) of 18 and 130 is 2, as it is the only common factor found through prime factorization. The prime factors of 18 are 2 and 3, while those of 130 are 2, 5, and 13. Therefore, GCF ( 18 , 130 ) = 2 .
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