Practice Questions
Find the HCF of 252 and 378 using Euclid's algorithm.
$378 = 252 \times 1 + 126$; $252 = 126 \times 2 + 0$. The last divisor is 126.
Find the HCF of $(2^4 \times 3^3 \times 5)$ and $(2^3 \times 3^4 \times 7)$.
Common factors are 2 and 3. HCF is the product of lowest powers: $2^3 \times 3^3 = 8 \times 27 = 216$.
Find the greatest number that divides 867 and 255 leaving remainder 3 in each case.
The number must divide $(867-3)=864$ and $(255-3)=252$. $\text{HCF}(864, 252) = 36$.
Find the HCF of 0.36 and 0.48.
Treat as 36 and 48. $\text{HCF}(36, 48) = 12$. Adjusting decimal places, we get 0.12.
Find the HCF of $5/12$ and $7/18$.
$\text{HCF} = \text{HCF}(5, 7) / \text{LCM}(12, 18) = 1 / 36$.
Two numbers have HCF 16 and product 4096. If one number is 64, find the other.
Product of numbers = $n_1 \times n_2 = 4096$. If $n_1 = 64$, then $n_2 = 4096 / 64 = 64$.
Find the HCF of 96, 144 and 240.
$\text{HCF}(96, 144) = 48$. $\text{HCF}(48, 240) = 48$.
Find the greatest number which divides 1251 and 937 leaving the same remainder.
Subtract the numbers: $1251 - 937 = 314$. The greatest number leaving the same remainder must divide the difference. Here, 314 itself works.
Find the HCF of polynomials: $(x^2 - 9)$ and $(x^2 - 6x + 9)$.
$(x^2 - 9) = (x-3)(x+3)$. $(x^2 - 6x + 9) = (x-3)^2$. The common factor is $(x-3)$.
Find the HCF of 148 and 185.
$185 = 148 \times 1 + 37$; $148 = 37 \times 4 + 0$. HCF = 37.
Premium Content
Unlock HCF Quiz and all premium lessons with a subscription.
From ₹199.99/year — See plans