If two positive integers a and b are expressible in the form a = pq^2 and b = p^3 q; p, q being prime number, then HCF (a, b) is

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Find the HCF of a = pq2 and b = p3q Video Explanation Watch the video below for a clear explanation: Solution Question: If two positive integers a and b are expressible in the form a = p q2 b = p3 q where p and q are prime numbers, find HCF(a, b). Step 1: […]

If two positive integers a and b are expressible in the form a = pq^2 and b = p^3 q; p, q being prime number, then HCF (a, b) is Read More »

If two positive integers a and b are expressible in the form a = pq^2 and b = p^3 q; p, q being prime number, then LCM (a, b) is

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Find the LCM of a = pq2 and b = p3q Video Explanation Watch the video below for a clear explanation: Solution Question: If two positive integers a and b are expressible in the form a = p q2 b = p3 q where p and q are prime numbers, find LCM(a, b). Step 1:

If two positive integers a and b are expressible in the form a = pq^2 and b = p^3 q; p, q being prime number, then LCM (a, b) is Read More »

The number of decimal place after which the decimal expansion of the rational number 23/2^2×5 will terminate, is (a) 1 (b) 2 (c) 3 (d) 4

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Number of Decimal Places in the Decimal Expansion of 23/(22 × 5) Video Explanation Watch the video below for a clear explanation: Solution Question: The number of decimal places after which the decimal expansion of the rational number 23 / (22 × 5) will terminate, is: (a) 1    (b) 2    (c) 3   

The number of decimal place after which the decimal expansion of the rational number 23/2^2×5 will terminate, is (a) 1 (b) 2 (c) 3 (d) 4 Read More »

The sum of the exponents of the prime factors in the prime factorisation of 196, is (a) 1 (b) 2 (c) 4 (d) 6

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Find the Sum of the Exponents of the Prime Factors of 196 Video Explanation Watch the video below for a clear explanation: Solution Question: The sum of the exponents of the prime factors in the prime factorisation of 196 is: (a) 1    (b) 2    (c) 4    (d) 6 Step 1: Prime Factorisation

The sum of the exponents of the prime factors in the prime factorisation of 196, is (a) 1 (b) 2 (c) 4 (d) 6 Read More »

If n = 2^3 ✕ 3^4 ✕ 5^4 ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is (a) 2 (b) 3 (c) 4 (d) 7

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Find the Number of Consecutive Zeros in n = 23 × 34 × 54 × 7 Video Explanation Watch the video below for a clear explanation: Solution Question: If n = 23 × 34 × 54 × 7 then the number of consecutive zeros in n, where n is a natural number, is: (a) 2

If n = 2^3 ✕ 3^4 ✕ 5^4 ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is (a) 2 (b) 3 (c) 4 (d) 7 Read More »

The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a) 600 (b) 500 (c) 400 (d) 200

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Which Value Cannot Be the HCF When the LCM Is 1200? Video Explanation Watch the video below for a clear explanation: Solution Question: The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a) 600    (b) 500    (c) 400    (d) 200 Important Property The HCF of two

The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a) 600 (b) 500 (c) 400 (d) 200 Read More »

The exponent of 2 in the prime factorisation of 144, is (a) 4 (b) 5 (c) 6 (d) 3

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Find the Exponent of 2 in the Prime Factorisation of 144 Video Explanation Watch the video below for a clear explanation: Solution Question: The exponent of 2 in the prime factorisation of 144 is: (a) 4    (b) 5    (c) 6    (d) 3 Step 1: Prime Factorisation of 144 144 = 12 ×

The exponent of 2 in the prime factorisation of 144, is (a) 4 (b) 5 (c) 6 (d) 3 Read More »

A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q when this number is expressed in the form p/q? Give reasons.

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Prime Factors of the Denominator of a Rational Number with Decimal Expansion 327.7081 Video Explanation Watch the video below for the complete explanation: Solution Question: A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q when this number is expressed in the form p/q? Give reasons.

A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q when this number is expressed in the form p/q? Give reasons. Read More »

What can you say about the prime factorizations of the denominators of the following rational numbers: (i) 43.123456789 (ii) 43.123456789 (iii) 27.142857 (iv) 0.120120012000120000….

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Prime Factorization of Denominators from Given Decimal Expansions Video Explanation Watch the video below for the complete explanation: Solution Question: What can you say about the prime factorizations of the denominators of the following rational numbers? Important Facts • A terminating decimal has denominator of the form 2m × 5n. • A non-terminating repeating decimal

What can you say about the prime factorizations of the denominators of the following rational numbers: (i) 43.123456789 (ii) 43.123456789 (iii) 27.142857 (iv) 0.120120012000120000…. Read More »

Write the denominator of the rational number 257/5000 in the form 2^m × 5^n, where m and n are non-negative integers. Hence, write the decimal expansion without actual division.

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Write the Denominator of 257/5000 in the Form 2m × 5n and Find Its Decimal Expansion Video Explanation Watch the video below for the complete explanation: Solution Question: Write the denominator of the rational number 257/5000 in the form 2m × 5n, where m and n are non-negative integers. Hence, write the decimal expansion without

Write the denominator of the rational number 257/5000 in the form 2^m × 5^n, where m and n are non-negative integers. Hence, write the decimal expansion without actual division. Read More »