Use prime factorization to find the HCF and LCM of 180 and 300
HCF = 2^2 * 3 * 5 = 60
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.
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.