Use prime factors to determine the HCF of \( 28 ; 196 \) and 280

To find the highest common factor (HCF) using prime factors, we start by finding the prime factorization of each number. - For \( 28 \): - \( 28 = 2 \times 14 = 2 \times 2 \times 7 = 2^2 \times 7^1 \) - For \( 196 \): - \( 196 = 2 \times 98 = 2 \times 2 \times 49 = 2^2 \times 7^2 \) - For \( 280 \): - \( 280 = 2 \times 140 = 2 \times 2 \times 70 = 2^3 \times 5 \times 7^1 \) Now, we take the lowest power of all common prime factors: - For \( 2 \): minimum power is \( 2^2 \) - For \( 7 \): minimum power is \( 7^1 \) Thus, the HCF is: \[ HCF = 2^2 \times 7^1 = 4 \times 7 = 28 \] So, the HCF of \( 28 \), \( 196 \), and \( 280 \) is \( 28 \).