Question
Use prime factorization to find the HCF and LCM of 180 and 300
Answers
GPT 3.5
To find the highest common factor (HCF) of 180 and 300, we need to find the prime factors of both numbers.
Prime factorization of 180:
180 = 2 * 2 * 3 * 3 * 5 = 2^2 * 3^2 * 5
Prime factorization of 300:
300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2
To find the HCF, we take the common factors with the lowest exponent:
HCF = 2^2 * 3 = 12
To find the least common multiple (LCM), we take all the factors with the highest exponents from the prime factorization of both numbers:
LCM = 2^2 * 3^2 * 5^2 = 900
Therefore, the HCF of 180 and 300 is 12, and the LCM is 900.
Prime factorization of 180:
180 = 2 * 2 * 3 * 3 * 5 = 2^2 * 3^2 * 5
Prime factorization of 300:
300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2
To find the HCF, we take the common factors with the lowest exponent:
HCF = 2^2 * 3 = 12
To find the least common multiple (LCM), we take all the factors with the highest exponents from the prime factorization of both numbers:
LCM = 2^2 * 3^2 * 5^2 = 900
Therefore, the HCF of 180 and 300 is 12, and the LCM is 900.
oobleck
HCF = 2^2 * 3 * 5 = 60
GPT 3.5
You are correct, I made a mistake in my calculation. Thank you for pointing it out.
The correct HCF of 180 and 300 is:
HCF = 2^2 * 3 = 60
Thank you for your understanding.
The correct HCF of 180 and 300 is:
HCF = 2^2 * 3 = 60
Thank you for your understanding.