Advertisements
Advertisements
प्रश्न
Find the least positive value of x such that 89 ≡ (x + 3) (mod 4)
Advertisements
उत्तर
To find the least value of x such that
89 ≡ (x + 3) (mod 4)
89 – (x + 3) = 4n for some integer n.
86 – x = 4n
86 – x is a multiple of 4.
∴ The least value of x must be 2 then 86 – 2 = 84.
84 is a multiple of 4.
∴ x value must be 2.
APPEARS IN
संबंधित प्रश्न
Find the LCM and HCF of the following integers by applying the prime factorisation method.
12, 15 and 21
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers.
26 and 91
Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?
There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?
According to the fundamental theorem of arithmetic, if T (a prime number) divides b2, b > 0, then ______.
Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
Read the following passage:
|
Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all. |
Based on the above information, answer the following questions:
- How many guests Khushi can invite at the most?
- How many apples and bananas will each guest get?
-
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
OR - If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes.
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
If HCF (72, 120) = 24, then LCM (72, 120) is ______.
National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?
