The HCF of 2 no is 70. Their product is 49000. What is the difference between the 2 numbers.
To find the difference between the two numbers, we need to first determine the two numbers themselves.
Let's start by finding the prime factorization of 49,000:
49,000 = 2 * 2 * 2 * 5 * 5 * 7 * 7 * 7
Since the highest common factor (HCF) of the two numbers is 70, we know that both numbers must contain at least one factor of 2, one factor of 5, and three factors of 7. However, we need to distribute the remaining factors between the two numbers in a way that maximizes their difference.
Let's assign the factors to each number:
Number 1: 2 * 5 * 7 * 7 = 490
Number 2: 2 * 2 * 7 * 7 = 196
To find the difference between the two numbers, simply subtract:
490 - 196 = 294
Therefore, the difference between the two numbers is 294.
To find the difference between the two numbers, we need to know the numbers themselves. Let's say the two numbers are A and B.
First, let's find the two numbers that have a HCF (Highest Common Factor) of 70 and a product of 49000.
The product of two numbers (A and B) is equal to their HCF multiplied by their LCM (Least Common Multiple).
So, in this case, 49000 is equal to 70 multiplied by the LCM of the two numbers:
49000 = 70 * LCM
To find the LCM, we need to divide 49000 by the HCF (70):
LCM = 49000 / 70
LCM = 700
Now, we have the LCM as 700. We need to find two numbers whose product is 49000 and LCM is 700.
To do that, we can use the equation:
LCM = (A * B) / HCF
By substituting the values, we get:
700 = (A * B) / 70
Simplifying the equation, we can multiply both sides by 70:
49000 = A * B
We know that the product of the two numbers (A and B) is 49000.
To find the two numbers (A and B), we can factorize 49000 into its prime factors:
49000 = 2 * 2 * 2 * 5 * 5 * 7 * 7
Now, we need to divide these factors into two numbers such that their product is 49000.
One possible combination is:
A = (2 * 2 * 5 * 5 * 7) = 700
B = (2 * 7 * 7) = 98
So, the two numbers are A = 700 and B = 98.
To find the difference between the two numbers, we subtract the smaller number from the larger number:
Difference = A - B = 700 - 98 = 602.
Therefore, the difference between the two numbers is 602.
The two numbers are 70m and 70n, where m and n have no common factors.
(70m)(70n) = 4900mn = 49000 = 4900*10
Thus, mn=10.
So, m and n are 2 and 5, or 1 and 10.