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Find the H.C. F of the following numbers using prime factors using prime factorization method:
(i) 144 and 198
Prime factorization of 144 = 2 × 2 × 2 × 3 × 3
Prime factorization of 198 = 2 × 3 × 3 ×11
Therefore, HCF = 2 × 2 × 3 = 18
(ii) 81 and 117
Prime factorization of 81 = 3 × 3 × 3 × 3
Prime factorization of 117 = 3 × 3 ×13
Therefore, HCF = 3 × 3 = 9
(iii) 84 and 98
Prime factorization of 84 = 2 × 2 × 3 × 7
Prime factorization of 98 = 2 × 7 × 7
Therefore, HCF = 2 × 7 = 14
(iv) 225 and 450
Prime factorization of 225 = 3 × 3 × 5 × 5
Prime factorization of 198 = 2 × 3 × 3 × 5 × 5
Therefore, HCF = 3 × 3 × 5 × 5 = 225
(v) 170 and 238
Prime factorization of 170 = 2 × 5 × 17
Prime factorization of 238 = 2 × 7 × 17
Therefore, HCF = 2 × 17 = 34
(vi) 504 and 980
Prime factorization of 504 = 2 × 2 × 2 × 3 × 3 × 7
Prime factorization of 980 = 2 × 2 × 5 × 7 × 7
Therefore, HCF = 2 × 2 × 7 = 28
(vii) 150, 140 and 210
Prime factorization of 150 = 2 × 3 × 5 × 5
Prime factorization of 140 = 2 × 2 × 5 × 7
Prime factorization of 210 = 2 × 3 × 5 × 7
Therefore, HCF = 2 × 5 = 10
(viii) 84, 120 and 138
Prime factorization of 120 = 2 × 2 × 2 × 3 × 5
Prime factorization of 138 = 2 × 3 × 23
Therefore, HCF = 2 × 3 = 6
(i×) 106, 159 and 265
Prime factorization of 106 = 2 × 53
Prime factorization of 159 = 2 × 53
Prime factorization of 265 = 5 × 53
Therefore, HCF = 53
What is the H.C.F of two consecutive?
(i) The common factor of two consecutive numbers is always 1.
Therefore, HCF of two consecutive numbers = 1
(ii) The common factors of two consecutive even numbers are 1 and 2.
Therefore, HCF of two consecutive even numbers = 2
(iii) The common factor of two consecutive odd numbers is 1.
Therefore, HCF of two consecutive odd numbers = 1
H.C.F of co-primes numbers 4 and 15 was found as follows:
4 = 2 × 2 and 15 = 3 × 5
Since there is no common prime factor. So, H.C.F of 4 and 15 is 0. Is the answer correct? If not what is the correct H.C.F?
No, it is not correct.
We know that HCF of two co-prime number is 1.
4 and 15 are co-prime numbers because the only factor common to them is 1.
Thus, HCF of 4 and 15 is 1.
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Chapter 2: Playing With Numbers – Exercise...