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To find the greatest common factor (GCF) of 324, 180, and 120 using prime factorization, we first break down each number into its prime factors.
324 = 2^2 * 3^4 180 = 2^2 * 3^2 * 5 120 = 2^3 * 3 * 5
Next, we identify the common prime factors among the numbers: 2^2, 3, and 5.
Multiplying these common prime factors together, we get the GCF: 2^2 * 3 * 5 = 60.
Therefore, the GCF of 324, 180, and 120 using prime factorization is 60.
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What is the prime factorization of 180 using exponents?
Prime factorization of 180 is: 2 * 2 * 3 * 3 * 5 Using all possible exponents, 22 * 32 * 522 x 32 x 5 = 180
What is the HCF of 120 and 180?
The Highest Common Factor (HCF) of 120 and 180 is the largest number that divides both 120 and 180 without leaving a remainder. To find the HCF, we need to factorize both numbers into their prime factors. The prime factorization of 120 is 2^3 * 3 * 5, and the prime factorization of 180 is 2^2 * 3^2 * 5. To find the HCF, we take the product of the common prime factors with the lowest exponent, which is 2^2 * 3 = 12. Therefore, the HCF of 120 and 180 is 12.
Prime factorization for 180?
180 = 2 * 2 * 3 * 3 * 5
Why is the prime factorization of 180 2x2x3x3x5?
2, 3, and 5 are all prime numbers and that is the only set of prime numbers that multiples to 180.
What is the LCM of 12 9 and 15?
To find the Least Common Multiple (LCM) of 12, 9, and 15, we first need to find the prime factorization of each number. The prime factorization of 12 is 2^2 * 3, the prime factorization of 9 is 3^2, and the prime factorization of 15 is 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^2 * 3^2 * 5 = 180. Therefore, the LCM of 12, 9, and 15 is 180.
