Advertisements
Advertisements
प्रश्न
Show that 107 is of the form 4q +3 for any integer q
उत्तर
107 = 4 × 26 + 3.
This is of the form a = bq + r.
Hence it is proved.
APPEARS IN
संबंधित प्रश्न
Prove that if a positive integer is of the form 6q + 5, then it is of the form 3q + 2 for some integer q, but not conversely.
Find the HCF of the following pairs of integers and express it as a linear combination of 506 and 1155.
If the HCF of 408 and 1032 is expressible in the form 1032 m − 408 × 5, find m.
15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?
Using prime factorization, find the HCF and LCM of 17,23,29 .
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `171/800`
Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.
(i)`64/455`
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF (525, 3000)? Justify your answer.
Prove that one of any three consecutive positive integers must be divisible by 3.
