Question

Three positive integers a, b and c have, in pairs, highest common factors (a,b) = 24,...

Three positive integers a, b and c have, in pairs, highest common factors

(a,b) = 24, (b,c) = 198 and (a,c) = 210.

(a) What is the highest common factor of a, b and c?

(b) Find the smallest values of a, b and c which satisfy the given criteria.

Homework Answers

Answer #1

I have solved the problem if you have any problem with the solution then please tell me on the comment box

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The least common multiple of nonzero integers a and b is the smallest positive integer m...
The least common multiple of nonzero integers a and b is the smallest positive integer m such that a | m and b | m; m is usually denoted [a,b]. Prove that [a,b] = ab/(a,b) if a > 0 and b > 0.
Give an example of three positive integers m, n, and r, and three integers a, b,...
Give an example of three positive integers m, n, and r, and three integers a, b, and c such that the GCD of m, n, and r is 1, but there is no simultaneous solution to x ≡ a (mod m) x ≡ b (mod n) x ≡ c (mod r). Remark: This is to highlight the necessity of “relatively prime” in the hypothesis of the Chinese Remainder Theorem.
1. (a) Let a, b and c be positive integers. Prove that gcd(ac, bc) = c...
1. (a) Let a, b and c be positive integers. Prove that gcd(ac, bc) = c x gcd(a, b). (Note that c gcd(a, b) means c times the greatest common division of a and b) (b) What is the greatest common divisor of a − 1 and a + 1? (There are two different cases you need to consider.)
Three positive integers (a, b, c) with a<b<c are called a Pythagorean triple if the sum...
Three positive integers (a, b, c) with a<b<c are called a Pythagorean triple if the sum of the square of a and the square of b is equal to the square of c. Write a program that prints all Pythagorean triples (one in a line) with a, b, and c all smaller than 1000, as well the total number of such triples in the end. Arrays are not allowed to appear in your code. Hint: user nested loops (Can you...
Three positive integers (a, b, c) with a<b<c are called a Pythagorean triple if the sum...
Three positive integers (a, b, c) with a<b<c are called a Pythagorean triple if the sum of the square of a and the square of b is equal to the square of c. Write a program that prints all Pythagorean triples (one in a line) with a, b, and c all smaller than 1000, as well the total number of such triples in the end. Arrays are not allowed to appear in your code. Hint: user nested loops (Can you...
Consider three positive integers, x1, x2, x3, which satisfy the inequality below: x1 + x2 +...
Consider three positive integers, x1, x2, x3, which satisfy the inequality below: x1 + x2 + x3 = 17. Let’s assume each element in the sample space (consisting of solution vectors (x1, x2, x3) satisfying the above conditions) is equally likely to occur. For example, we have equal chances to have (x1, x2, x3) = (1, 1, 15) or (x1, x2, x3) = (1, 2, 14). What is the probability the events x1 + x2 ≤ 8 occurs, i.e., P(x1...
Problem Definition: Problem: Given an array of integers find all pairs of integers, a and b,...
Problem Definition: Problem: Given an array of integers find all pairs of integers, a and b, where a – b is equal to a given number. For example, consider the following array and suppose we want to find all pairs of integers a and b where a – b = 3 A = [10, 4, 6, 16, 1, 6, 12, 13] Then your method should return the following pairs: 4, 1 15, 12 13, 10 A poor solution: There are...
24. Which substance would be predicted to have the highest boiling point? A) CH4 B) KI...
24. Which substance would be predicted to have the highest boiling point? A) CH4 B) KI C) CS2 D) HF E) I2
(a) Show that the following algorithm computes the greatest common divisor g of the positive integers...
(a) Show that the following algorithm computes the greatest common divisor g of the positive integers a and b, together with a solution (u, v) in integers to the equation au + bv = gcd(a, b). 1. Set u = 1, g = a, x = 0, and y = b 2. If y = 0, set v = (g − au)/b and return the values (g, u, v) 3. Divide g by y with remainder, g = qy +...
a) How many positive divisors does 144 have? b) What is the sum of the positive...
a) How many positive divisors does 144 have? b) What is the sum of the positive divisors of 144? c) Which positive integers have an odd number of positive divisors? (Prove your answer)