Find the GCF of the numbers using an appropriate method.
240, 10,000, and 4500
Find the prime factorization of the number, and write it in exponent form.
670
Find the LCM for the given numbers by an appropriate method.
24, 54, and 27
To find the Greatest Common Factor (GCF) of the numbers 240, 10,000, and 4500, we can use the prime factorization method.
1. Find the prime factorization of each number:
- Prime factorization of 240: 2^4 * 3 * 5
- Prime factorization of 10,000: 2^4 * 5^4
- Prime factorization of 4500: 2^2 * 3^2 * 5^3
2. Identify the common prime factors and their lowest exponents among the numbers. In this case, the common prime factors are 2 and 5, with the lowest exponents being 2 and 1, respectively.
3. Multiply the common prime factors with their lowest exponents. GCF = 2^2 * 5^1 = 20.
Therefore, the GCF of 240, 10,000, and 4500 is 20.
To find the prime factorization of the number 670, we can use the following steps:
1. Start by dividing the number by the smallest prime factor, which is 2. However, since 670 is an odd number, it's not divisible by 2.
2. Move on to the next prime number, which is 3. We divide 670 by 3 and get 223. Since 223 is a prime number, we stop here.
3. The prime factorization of 670 is therefore 2^1 * 3^0 * 223^1, or simply 2 * 223.
To find the Least Common Multiple (LCM) of the numbers 24, 54, and 27, we can use the prime factorization method.
1. Find the prime factorization of each number:
- Prime factorization of 24: 2^3 * 3^1
- Prime factorization of 54: 2^1 * 3^3
- Prime factorization of 27: 3^3
2. Identify all the prime factors with their highest exponents among the numbers. In this case, the prime factors are 2^3 and 3^3.
3. Multiply the prime factors with their highest exponents. LCM = 2^3 * 3^3 = 8 * 27 = 216.
Therefore, the LCM of 24, 54, and 27 is 216.
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
Find the GCF of the numbers using an appropriate method.
240, 10,000, and 4500
Find the prime factorization of the number, and write it in exponent form.
670
Find the LCM for the given numbers by an appropriate method.
24, 54, and 27