Advertisements
Advertisements
प्रश्न
Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.
उत्तर
The required number when divides 280 and 1245 leaves the remainder 4 and 3, this means 280 4 – 216 and 1245 – 3 = 1245 – 3 = 1242 are completely divisible by the number
∴ The required number = HCF of 276 and 1242
By applying Euclid’s division lemma
1242 = 276 × 4 + 138
276 = 138 × 2 + 0
∴ HCF = 138
Hence the required numbers is 138.
APPEARS IN
संबंधित प्रश्न
Show that any positive odd integer is of the form 6q + 1 or, 6q + 3 or, 6q + 5, where q is some integer.
Define HOE of two positive integers and find the HCF of the following pair of numbers:
155 and 1385
Define HOE of two positive integers and find the HCF of the following pair of numbers:
100 and 190
Define HOE of two positive integers and find the HCF of the following pair of numbers:
105 and 120
Find the HCF of the following pairs of integers and express it as a linear combination of 1288 and 575.
What is a composite number?
Prove that following numbers are irrationals:
If HCF of 65 and 117 is expressible in the form 65n − 117, then find the value of n.
Show that the square of any odd integer is of the form 4q + 1, for some integer q.
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
[Hint: Any positive integer can be written in the form 5q, 5q + 1, 5q + 2, 5q + 3, 5q + 4].
