Quick Mental Math Hack Multiplication by using Line Revealed
🧮 Easy Multiples
Did you know you can use simple line tricks? This simple trick makes multiplication a breeze.
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Solving LCM and HCF Puzzles: Finding the Number of Pairs
Learn how LCM and HCF concepts help you solve complex problems, find the number of pairs, determine divisors and factors, and crack math puzzles. Enhance your number theory skills and boost your chances of success in these competitive exams. Don’t miss out on this essential topic that can make a significant difference in your exam performance!
Que: How many pairs of integers (x,y) exist such that the product of x,y, and HCF(x,y)= 1080?
(a) 8
(b) 7
(c) 9
(d) 12
Total Pairs=9
Option (c) is correct.
Que: Find the least number that should be added to 2014 such that the resulting number can be divided by 3,4,5, and 6 leaving no remainder.
(a) 34
(b) 60
(c) 36
(d) 26
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The LCM and HCF concepts are very useful in solving problems involving fractions, simplifying algebraic expressions, and finding solutions to equations. Some questions based on LCM and HCF concepts are as follows:
Find the LCM and HCF of two or more numbers
Simplification of fractions
Find the smallest or largest number satisfying given conditions
Calculate the time taken by two or more persons to complete a task working together.
Total number of rotations or revolutions required by two or more wheels to come back to their initial position
Find the least n-digit number which when divided by the given numbers leaves the same or different remainder.
How many pairs of numbers are there whose product is given
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In this article, we will explore the divisor concepts, including the number of factors, prime factors, and the fascinating properties of the sum and product of factors. By understanding these concepts, you will gain valuable insights into the relationships between numbers and unlock the secrets hidden within their divisors.
The divisor or factor of any number divides it without leaving any remainder. For example, let’s consider the number 12. The divisors or factors of 12 are 1,2,3,4,6 and 12.
To find the total number of divisors of any number, we use the prime factorization method given below.
For example, the prime factorization of any number (N) is p^a×q^b×r^c, Here p,q, and r are the prime numbers (2,3,5,7,11,…etc.) and a,b, and c are their respective exponents.
The total number of divisors of N= (a+1)×(b+1)×(c+1)