Express each number as a product of its prime factors: (i) 140, (ii) 156, (iii) 3825, (iv) 5005, (v) 7429
(i) \(2^2 \times 5 \times 7\)
(ii) \(2^2 \times 3 \times 13\)
(iii) \(3^2 \times 5^2 \times 17\)
(iv) \(5 \times 7 \times 11 \times 13\)
(v) \(17 \times 19 \times 23\)
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers:
(i) 26 and 91, (ii) 510 and 92, (iii) 336 and 54.
(i) LCM = 182; HCF = 13
(ii) LCM = 23460; HCF = 2
(iii) LCM = 3024; HCF = 6
Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21, (ii) 17, 23 and 29, (iii) 8, 9 and 25.
(i) LCM = 420; HCF = 3
(ii) LCM = 11339; HCF = 1
(iii) LCM = 1800; HCF = 1
Given that HCF(306, 657) = 9, find LCM(306, 657).
22338
Check whether \(6^n\) can end with the digit 0 for any natural number \(n\).
\(6^n\) cannot end with 0 because it always ends with 6 for all natural numbers \(n\).
Explain why \(7 \times 11 \times 13 + 13\) and \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5\) are composite numbers.
\(7 \times 11 \times 13 + 13 = 13(7 \times 11 + 1)\) is composite. \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5 = 5040 + 5 = 5045 = 5 \times 1009\) is also composite.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time. When will they meet again at the starting point?
36 minutes