Find the best tutors and institutes for Class 10 Tuition
Search in
Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
(iv)
Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
HCF , LCM=
HCF , LCM
HCF , LCM
Given that HCF (306, 657) = 9, find LCM (306, 657).
Product of HCF and LCM of 2 numbers=product of these numbers
HCF=9
LCM=?
first number=306
second number=657
so,
9 X LCM=306 X 657
LCM=
LCM =22338
Check whether 6n can end with the digit 0 for any natural number n.
f any number ends with the digit 0, it should be divisible by 10 or in other words its prime factorisation must include primes 2 and 5 both
Prime factorisation of 6n = (2 x 3)n
By Fundamental Theorem of Arithmetic Prime factorisation, every number is unique. So 5 is not a prime factor of 6n.
Hence, for any value of n, 6n will not be divisible by 5.
Therefore, cannot end with the digit 0 for any natural number n.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Ravi and Sonia donot take the same amount of time.
Ravi takes lesser time than Sonia for completing 1 round of the circular path.
As they are going in the same direction, they meet again at the same time when Ravi will have completed 1 round of that circular path with respect to Sonia.
i.e When Sonia completes one round then Ravi completes 1.5 rounds.
The minimum time when Sonia and Ravi meet again will be the LCM Of 18 minutes and 12 minutes
Now
18 = 2 x 3 x 3 = 2 x 32
And, 12 = 2 x 2 x 3 = 22 x 3
LCM of 12 and 18 = product of factors raised to highest exponent =
22 x 32 = 36
Therefore, Ravi and Sonia will meet together at the starting point after 36 minutes.
Explain why 7*11*13+13 and 7*6*5*4*3*2*1+5 are composite numbers.
Observe that,
7 x 11 x 13 + 13 = 13 x (7 x 11 + 1) = 13 x (77 + 1)
= 13 x 78
= 13 x 13 x 6
The given expression has 6 and 13 as its factors. Therefore, it is a composite number.
7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = 5 x (7 x 6 x 4 x 3 x 2 x 1 + 1)
= 5 x (1008 + 1)
= 5 x 1009
1009 cannot be factorised further. Therefore, the given expression has 5 and 1009 as its factors. Hence, it is a composite number.
Find the LCM and HCF of the following pairs of integers and verify that LCM*HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
HCF
Now, HCF X LCM =
Product of two numbers
From (i) and (ii) it implies that Product of the 2 numbers
Hence verified.
HCF =
Now,
Product of the numbers, ......
From (i) and (ii) it implies that Product of the 2 numbers
Hence verified.
HCF=6, LCM =
NOw, HCF X LCM
Product of the numbers,
From (i) and (ii) it implies that Product of the 2 numbers
Hence verified.
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 10 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 10 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class
