Which of the following is a pair of co-primes?
25 and 36
Two numbers are co-prime if their highest common factor (HCF) is 1.
\(25 = 5^2\) and \(36 = 2^2 \times 3^2\); they share no common prime factor, so \(\text{HCF}(25,36) = 1\).
\(44 = 2^2 \times 11\) and \(99 = 3^2 \times 11\) share the factor 11, so their HCF is 11, not co-prime.
\(27 = 3^3\) and \(36 = 2^2 \times 3^2\) share the factor 3, so they are not co-prime.
\(42 = 2 \times 3 \times 7\) and \(56 = 2^3 \times 7\) share factors 2 and 7, so they are not co-prime.
Hence, 25 and 36 form a pair of co-primes.
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Important Questions from LCM and HCF
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A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
