Example Question - hcf
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Finding Highest Common Factor by Prime Factorization Method
The question is asking for the highest common factor (HCF), also known as the greatest common divisor (GCD), of the given numbers using the prime factorization method. Let's solve each part one by one: (a) Find the HCF of 12 and 16. First, we find the prime factors of the numbers 12 and 16. 12 = 2 x 2 x 3 (which is also written as \( 2^2 \times 3 \)) 16 = 2 x 2 x 2 x 2 (which is \( 2^4 \)) Now, we look for the common prime factors, which are the factors that are the same in both prime factorizations. The common prime factors are two 2's (since 2^2 is the highest power of 2 that divides both 12 and 16). The HCF is therefore 2 x 2 = 4. (b) Find the HCF of 36 and 90. Now let's find the prime factors of 36 and 90. 36 = 2 x 2 x 3 x 3 (which is \( 2^2 \times 3^2 \)) 90 = 2 x 3 x 3 x 5 (which is \( 2 \times 3^2 \times 5 \)) The common prime factors for 36 and 90 are a 2, and two 3's. The HCF is therefore 2 x 3 x 3 = 18. So the answers are: (a) The HCF of 12 and 16 is 4. (b) The HCF of 36 and 90 is 18.
Math Solution: Finding Number B from Given Equation
Hai số A và B có Bội số chung nhỏ nhất (LCM) là 2.760 và Ước số chung lớn nhất (HCF) là 46. Ta biết rằng tích của hai số bằng tích của LCM và HCF của chúng. Điều này có thể viết là: A * B = LCM(A, B) * HCF(A, B) Thay số: A * B = 2.760 * 46 Vì A = 184, ta có thể tìm B bằng cách sắp xếp lại phương trình trên: B = (LCM(A, B) * HCF(A, B)) / A B = (2.760 * 46) / 184 Ta thực hiện phép tính: B = 127.760 / 184 B = 694 Vậy B = 694.
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