1 Marks Question

Question 11 Mark

If a and b are relatively prime numbers, then what is their LCM?

Answer

If a and b are relatively prime numbers, then their LCM is ab.
In LCM we choose all prime factor and if two numbers are relatively prime, so their factor is a and b.
So, LCM (a, b) = ab

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Question 21 Mark

Write the condition to be satisfied by q so that a rational number $\frac{\text{p}}{\text{q}}$ has a terminating decimal expansion.

Answer

In the rational number $\frac{\text{p}}{\text{q}},$ the factorization of denominator q must be in form of $2^m \times 5^n$ where m and n are non-negative integers.

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Question 31 Mark

What is a lemma?

Answer

A lemma is a proven statement which is used to prove other statement.

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Question 41 Mark

Given that HCF (306. 657) = 9, find LCM (306, 657).

Answer

By the property that LCM × HCF = Product of the two numbers
LCM × 9 = 306 × 657
LCM $=\frac{306\times 657}{9}= 22338$
Therefore LCM (306, 657) = 22338.

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Question 51 Mark

Determine the prime factorisation of the following positive integer:
$20570$

Answer

$20570 = 2 \times 5 \times 12^4 \times 17$

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Question 61 Mark

If p and q are two prime numbers, then what is their LCM?

Answer

If p and q are two primes, their LCM will be their product.

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Question 71 Mark

Express the following integers as a product of its prime factors:
$468$

Answer

To Express:
Each of the following numbers as a product of their prime factors.
$468 = 2^2 \times 3^2 \times 13$

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Question 81 Mark

Express the following integers as a product of its prime factors:
$945$

Answer

To Express:
Each of the following numbers as a product of their prime factors.
$945 = 3^3 \times 5 \times 7$

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Question 91 Mark

Express the following integers as a product of its prime factors:
$420$

Answer

To Express:
Each of the following numbers as a product of their prime factors.
$420 = 2^2 \times 3 \times 5 \times 7$

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Question 101 Mark

If a and b are relatively prime numbers, then what is their HCF?

Answer

a and b are relatively prime numbers than their HCF is 1 because in HCF we choose common prime factor and if two numbers are relatively prime then their common factor is 1.
HCF (a, b) = 1

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Question 111 Mark

What is the HCF of the smallest composite number and the smallest prime number?

Answer

We know that 2 is the smallest prime number and 4 is the smallest composite number HCF of 2 and 4 = 2

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Question 121 Mark

Determine the prime factorisation of the following positive integer:
$45470971$

Answer

$45470971 = 7^2 \times 13^2 \times 17^2 \times 19$

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Question 131 Mark

What is the total number of factors of a prime number?

Answer

Total number of factors of a prime number is 2 i.e., 1 and itself.

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Question 141 Mark

For what value of $n, 2^n \times 5^n$^ ends in $5.$

Answer

Solution:
$2^n \times 5^n$
If $n = 0$, then $2^0 \times 5^0 = 1 \times 1 = 1$
If $n = 1$, then $2^1 \times 5^1 = 2 \times 5 = 10$
If $n = 2$, then $2^2 \times 5^2 = 4 \times 25 = 100$
Thus, no value of $n, 2^n\times 5^n$ and in $5$.

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Question 151 Mark

Write the sum of the exponents of prime factors in the prime factorisation of $98.$

Answer

$98 = 2 \times 7 \times 7 = 2^1 \times 7^2$
Sum of exponents$ = 1 + 2 = 3$

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Question 161 Mark

What is an algorithm?

Answer

Algorithm: An algorithm is a series of well defined slips which gives a procedure for solving a type of problem.

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Question 171 Mark