Write the HCF of smallest composite number and smallest prime number.
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Find the LCM and HCF of the following pairs of integer and verify that LCM×HCF=Product of the two numbers.
Solution : i) 26 and 91 26=2×13×1(expressing as product of it’s prime factors) 91=7×13×1(expressing as product of it’s prime factors) So, LCM(26,91)=2×7×13×1=182 HCF(26,91)=13×1=13 Verification: LCM×HCF=13×182=2366 Product of 26 and 91 =2366 Therefore,LCM×HCF=Product of the two numbers . i) 510 and...
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Find the LCM and HCF of the following integers by applying the prime factorization method. i) 12,15 and 21 ii) 17,23 and 29 iii) 8,9 and 25
Solution : i) 12,15 and 21 12=2×2×3 15=5×3 21=7×3 From the above ,HCF(12,15,21)=3and LCM(12,15,21)=420 ii)17,23,and 29 17=17×1 23=23×1 29=29×1 From the above ,HCF(17,23,29)=1and LCM(17,23,29)=11339 iii)8,9 and 25 8=2×2×2 9=3×3 25=5×5 From the above ,HCF(8,9,25)=1and LCM(8,9,25)=1800
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If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find
A = {x: x is a natural number} = {1, 2, 3, 4, 5 …} B ={x: x is an even natural number} = {2, 4, 6, 8 …} C = {x:...
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A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number.
Answer Possible numbers of events on throwing a dice = 6 Numbers on dice = 1,2,3,4,5 and 6 (i) Prime numbers = 2, 3 and 5 Favourable number of events = 3 Probability that it...
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The HCF of 65 and 117 is expressible in the form 65m - 117. Find the value of m. Also find the LCM of 65 and 117 using prime factorization method.
Solution: 117 = 65 x 1 + 52 65 = 52 x 1 + 13 65 = 13 x 5 + 0 => HCF(65, 117) = 13 Since, HCF(65, 117) = 65m - 117 => 13 = 65m - 117 => 65m...
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If two positive integers a and b are written as a = x^3y^2 and b = xy^3; x, y are prime numbers, then HCF (a, b) is
Correct answer is (B) xy2
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π-22/7 is (A) a rational number (B) an irrational number (C) a prime number (D) an even number
It is (B) an irrational number
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Define HOE of two positive integers and find the HCF of the following pairs of numbers: (i) 32 and 54 (ii) 18 and 24 (iii) 70 and 30 (iv) 56 and 88
By applying Euclid’s division lemma (i) 54 = 32 × 1 + 22 Since remainder ≠ 0, apply division lemma on division of 32 and remainder 22. 32 = 22 × 1 +...
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Explain why 3 x 5 x 7+7 is a composite number.
3x5x7+7=7(3x5+1)=7x16, which has more than two factors.
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What is the probability that a number selected from the number 1 to 10 is not a prime number when each number is equally likely to be selected?
Total non-prime numbers from 1 to 10 = 6 Required probability =6/10=3/5
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