Advertisements
Advertisements
प्रश्न
Define HOE of two positive integers and find the HCF of the following pair of numbers:
56 and 88
उत्तर
By applying Euclid’s division lemma
88 = 56 × 1 + 32
Since remainder ≠ 0, apply division lemma on divisor of 56 and remainder 32.
56 = 32 × 1 + 24
Since remainder ≠ 0, apply division lemma on divisor of 32 and remainder 24.
32 = 24 × 1 + 8
Since remainder ≠ 0, apply division lemma on divisor of 24 and remainder 8.
24 = 8 × 3 + 0
∴ HCF of 56 and 88 is = 8.
APPEARS IN
संबंधित प्रश्न
Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.
If a and b are two odd positive integers such that a > b, then prove that one of the two numbers `(a+b)/2` and `(a-b)/2` is odd and the other is even.
The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
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?
Without actual division show that each of the following rational numbers is a non-terminating repeating decimal
(i) `73/(2^3× 3^3 × 5)`
Show that the following numbers are irrational.
Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4
Prove that two consecutive positive integers are always co-prime
“The product of three consecutive positive integers is divisible by 6”. Is this statement true or false”? Justify your answer.
Prove that if x and y are both odd positive integers, then x2 + y2 is even but not divisible by 4.
