Fundamental Theorem of Arithmetic

Q.

Check whether $6^n$ can end with the digit 0 for any natural number n.

Q. What is the largest number that divides 245 and 1029, leaving remainder 5 in each case ?

1. 16

Q.

If the HCF of $408$ and $1032$ is expressible in the form $1032m-408x5$. Find $m$.

Q.

Express $3825$ as a product of its prime factors.

Q. Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a measuring vessel that can be used to exactly measure the petrol from either tankers with no petrol remaining.

1. 200 litres
2. 170 litres
3. 440 litres
4. 360 litres

Q. Explain why $(17\times 5\times 11\times 3\times 2+2\times 11)$ is a composite number?

Q.

For what value of ‘n’ would $4^n$ end with zero?

1. It will not end with zero for any value of n.

2. 10

3. 0

4. Can’t say

Q.

Explain whether $(3\times 12\times 101)+4$ is a prime number or a composite number.

Q.

Find the HCF of $1260$and $7344$using Euclids division algorithm

Q.

Explain why $3\times 5\times 7+7$ is a composite number.

Q. For any natural number $n,4^n$ cannot end with which of the following?

1. 4
2. 6
3. \N
4. None of the above

Q.

Use Euclids division algorithm to find the HCF of $196$ and $38220$.

Q.

119² - 111² is:

1. An odd prime number

2. Composite number

3. An odd composite number

4. Prime number

Q.

Five bells begin to toll together and toll respectively at intervals of $6,5,7,10$ and $12$ seconds. How many times will they toll together in one hour excluding the one at the start.

1. $7$ times

2. $8$ times

3. $9$ times

4. $11$ times

Q. 3*5*13*46+23 is a prime number or a composite number.

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Q.

What Does M Mean In Maths?

Q.

What is $\frac{3}{4}$ of an hour?

Q. Every composite number can be factorised as a product of primes.

1. True
2. False

Q. Explain why 3 x 5 x 7 x 11 + 11 is a composite number ?

Q.

Question 29
If the number 7254*98 is divisible by 22, the digit at * is

(A) 1
(B) 2
(C) 6
(D) 0

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

Q.

Show that 5n cannot end with the digit 2

Q. Solve for x :
$\frac{1}{2x-3}+\frac{1}{x-5}=1\frac{1}{9},x\ne \frac{3}{2},5$

Q.

Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

1. Theorem of factorization

2. Composite Theorem

3. Euclid’s Theorem

4. Fundamental Theorem of Arithmetic

Q.

Use Euclids division algorithm to find the HCF of $900$ and $270$.

Q.

If the HCF of $85$and $153$ is expressible in the form of $85m-153$, the value of $m$ is

1. $1$

2. $2$

3. $3$

4. $4$

Q.

Number of common factors of 360 and 18144 are

1. 6

2. 10

3. 8

4. 9

Q. For any natural number $n,4^n$ cannot end with which of the following?

1. None of the above
2. 4
3. 6
4. 0

Q. For two numbers 96 and 404, the HCF is 4. What is the LCM of the two numbers?

1. 9696

Q.

How to convert $256$ into binary?