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Mathematics
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Determine the prime factorisation of the following positive integer:

 20570

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Determine the prime factorisation of the following positive integer:

58500

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

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Determine the prime factorisation of the following positive integer:

45470971

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers.

26 and 91

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Find the LCM and HCF of the following integers by applying the prime factorisation method:

40, 36 and 126

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Find the LCM and HCF of the following integers by applying the prime factorisation method:

 84, 90 and 120

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Find the LCM and HCF of the following integers by applying the prime factorisation method:

 24, 15 and 36

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where m, n are non-negative integers.

\[\frac{3}{8}\]

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where m, n are non-negative integers.

\[\frac{13}{125}\]

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where m, n are non-negative integers.

\[\frac{129}{2^2 \times 5^7}\]

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

State Fundamental Theorem of Arithmetic.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Write the exponent of 2 in the prime factorization of 144.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Write the sum of the exponents of prime factors in the prime factorization of 98.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

If the prime factorization of a natural number n is 23 × 32 × 52 × 7, write the number of consecutive zeros in n.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

If the product of two numbers is 1080 and their HCF is 30, find their LCM.

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Express the number as a product of its prime factor:

156

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Express the number as a product of its prime factor:

3825

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined

Express the number as a product of its prime factor:

5005

[1] Real Numbers
Chapter: [1] Real Numbers
Concept: undefined >> undefined
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