Advertisements
Advertisements
Question
Using prime factorization, find the HCF and LCM of 17,23,29 .
Solution
17 = 17
23 = 23
29 = 29
HCF = product of smallest power of each common prime factor in the numbers = 1
LCM = product of greatest power of each prime factor involved in the numbers
= 17 × 23 × 29 = 11339
APPEARS IN
RELATED QUESTIONS
Prove that the square of any positive integer of the form 5q + 1 is of the same form.
105 goats, 140 donkeys and 175 cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip and they have to be of the same kind. He will naturally like to take the largest possible number each time. Can you tell how many animals went in each trip?
Show that every positive even integer is of the form 4m and that every positive odd integer is of the form 4m + 1 for some integer m.
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `19/3125`
Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).
HCF of two numbers is always a factor of their LCM (True/False).
Every odd integer is of the form 2m − 1, where m is an integer (True/False).
For what value of n, 2n ✕ 5n ends in 5.
If HCF of 65 and 117 is expressible in the form 65n − 117, then find the value of n.
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF (525, 3000)? Justify your answer.