Factors

Q.

Every number is a factor of itself

1. True

2. False

Q. Find the number of factors and sum of factors of 25920 excluding 1 and itself.

Q.

Prime factorization of 1400:

1. ${2.3}^2{.5}^3$

2. $2^3.5.7$

3. $2^3{.5}^2{.7}^2$

4. $2^3{.5}^2.7$

Q. Express 140 as the product of its prime factors using factor tree.

Q.

Which of the following numbers has both 7 and 5 as factors?

1. 55

2. 28

3. 30

4. 70

Q.

Express each of the following numbers as the sum of two odd primes:

$100$

Q. Question 15
The value of ${249}^2–{248}^2$ is

A) $1^2$
B) $477$
C) $487$
​​​​​​​D) $497$

Q.

Express each of the following numbers as the sum of two odd primes:

$80$

Q. Question 3(i)
Express the number appearing in the following statements in standard form:
$1micronisequalto\frac{1}{1000000}m,$

Q.

Find the sum of divisors of 199584?

Q.

36 has _________ number of prime factors.

1. 3

2. 1

3. 4

4. 2

Q. the highest power of 2 by which the product of first hundred counting numbers can be divided without any remainder is 97 96 95 94

Q.

7. Fill in the blanks :

(iii) _________ is the only even prime number.

Q. The sum of all factors of 45000 which are exactly the multiples of 10 is

Q. Find the largest number which divides $320$ and $457$, leaving remainders $5$ and $7$ respectively.

Q. Determine the prime factorisation of 58500

1. 2 x 2 x 3 x 5 x 5 x 5 x 5 x 17
2. 2 x 2 x 3 x 3 x 5 x 5 x 5 x 17
3. 2 x 2 x 3 x 3 x 5 x 5 x 5 x 13
4. 2 x 3 x 3 x 3 x 5 x 5 x 5 x 13

Q.

Express the following numbers as sum of two odd prime numbers.

$36=\_\_\_\_+\_\_\_\_$

Q.

36 has _________ number of prime factors.

1. 1

2. 2

3. 3

4. 4

Q. Match the following numbers with the correct product of prime factors.
1. 1008
2. 784
3. 240

1. $2^4\times 3\times 5$
2. $2^4\times 7^2$
3. $2^4\times 3^2\times 7^1$

Q. Match the numbers to the product of its prime factors.

1. 2 × 2 × 3 × 13
2. 2 × 2 × 5 × 7
3. 3 × 37
4. 2 × 2 × 5 × 5

Q. Prime factorization of 48 is .

1. $2^4\times 3$
2. $6\times 8$
3. $2^3\times 3$

Q.

Find the common factors of : $4,8\mathrm{and}12$

Q. Match the numbers to the product of its prime factors.

1. 2 × 2 × 5 × 7
2. 2 × 2 × 3 × 13
3. 2 × 2 × 5 × 5
4. 3 × 37

Q.

Write the all factors of the following number.

$48$

Q.

Write all the factors of the following number.

$60$

Q. p is prime, n is a positive integer and n+p= 2000. L.C.M. of n and p is 21879 . Then find n and p

Q. While factorising 123, which of the the following is the least prime factor of 123?

1. 3
2. 41
3. 17
4. 1

Q. Express 140 as the product of its prime factors.

Q.

Check whether the first number is the factor of the second number, or not.

$8,72$

Q.

Prime factorization of 1400:

1. ${2.3}^2{.5}^3$

2. $2^3.5.7$

3. $2^3{.5}^2{.7}^2$

4. $2^3{.5}^2.7$