Prime Factorization

Q.

Decompose $32760$ into prime factors.

Q.

A number is divisible by both $5$ and $12$. By which another number will that number be always divisible?

Q. Question 3 (iii)
Find the LCM and HCF of 8, 9 and 25 by applying the prime factorization method.

Q.

Find the LCM of 12, 15 and 18 using prime factorisation method.

1. 180
2. 80
3. 90
4. 60

Q.

Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be of same height? [4 MARKS]

Q. Product of prime factors of 3, 024 is
2 x 2 x 2 x 2 x 3 x

1. 3 x 3 x 7
2. 2 x 3 x 7
3. 3 x 7 x 7
4. 3 x 21

Q. Identify the correct product of prime factors of 924.

1. 2 x 2 x 3 x 7
2. 2 x 3 x 7 x 11
3. 2 x 2 x 3 x 7 x 11
4. None of these

Q.

Find the LCM and HCF of 336 and 54

1. LCM = 6
2. HCF = 3024
3. LCM = 3024
4. HCF = 6

Q. 252 is evenly divisible by 9 and 3 but it is not evenly divisible by ​​

1. 2
2. 7
3. 27
4. 4

Q. Express the number as product of its prime factors
7429

1. $27\times 19\times 33$
2. $17\times 19\times 23$
3. $17\times 25\times 23$
4. $13\times 19\times 23$

Q.

LCM of 60, 45 is

1. 2 x 3 x 5

2. 2² x 3³

3. 2² x 3² x 5¹

4. 2³ x 3²

Q. Three bells toll at intervals of $9,12,15$ minute respectively. If they start tolling together after what time will they next toll together

Q.

Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be of same height?

1. 36

2. 6

3. 72

4. 18

Q.

What is the L.C.M of X and Y if X is the first odd prime number and Y is the only even prime number?

1. 6

2. 8

3. 2

4. 12

Q.

If 735 is divisible by , 5 and (ascending order) then it is also divisible by 15, 21 and 105.

1. 3
2. 4
3. 7
4. 2

Q. 1 is neither prime nor composite.

1. True
2. False

Q. Express each of the following numbers as a product of powers of their prime factors:
(i) 36
(ii) 675
(iii) 392

Q.

Find the LCM and HCF of the following integers by applying the prime factorization method : 17, 23 and 29

Q. Factorise the following numbers into primes.
(i) 342
(ii) 377
(iii) 559

Q. Find the LCM of the following integers by applying the prime factorization method
12, 15 and 21

1. $420$
2. $419$
3. $430$
4. $450$

Q. Pair the following as per divisibility rules.

1. last 3 digits
2. last 2 digits
3. units digit
4. sum of digits

Q.

Akashi was playing with the numbers. She found that a number is divisible by both 7 and 12.

Which is the least number of which both of these will be divisible? [3 MARKS]

Q. Find the prime factors of the following numbers and find their LCM and HCF: 75, 135 [2 Marks]

Q. Which of the following options do not represent a prime factorization?

1. 18 = $2\times 3\times 3$
2. 25 = $5\times 5$
3. 45 = $5\times 9$
4. 50 = $2\times 5\times 5$

Q. Pop the odd prime numbers

1. 2
2. 5
3. 7
4. 15
5. 19
6. 13
7. 25
8. 11

Q. If 7 and 11 are the prime factors of the fraction's denominator, then it's a repeating decimal number.

1. True
2. False

Q. Pop the prime factors of 2310.

1. 2
2. 6
3. 15
4. 3
5. 5
6. 7
7. 11
8. 9

Q. 252 can be expressed as a product of primes as:

1. 2 x 2 x 3 x 3 x 7​
2. 2 x 2 x 2 x 3 x 7
3. 2 x 3 x 3 x 3 x 7
4. 2 x 2 x 3 x 7 x 7

Q. A person is riding a bicycle at the speed of $17.6$ metre per second. Round this speed up to nearest natural number and find it's prime factorisation.

1. $2\times 3\times 3$
2. $2\times 2\times 2\times 2$
3. $17\times 1$
4. $2\times 2\times 5$

Q. Area of a plot is $693{\text{m}}^2.$ It is known that the length of the plot is a prime number. Find the possible value(s) of the length.

1. $3\text{m}$
2. $7\text{m}$
3. $9\text{m}$
4. $11\text{m}$