which greatest number when divided into 1250 and 1000 leaves a remainder of 26 and 28 respectively, can u submit the ans.?
Factor 1224 and 972.
See your following post.
To find the greatest number that satisfies the given conditions, we need to find the largest common divisor (GCD) of 1250-26 and 1000-28.
1250 (dividend) - 26 (remainder) = 1224
1000 (dividend) - 28 (remainder) = 972
Now we find the GCD of 1224 and 972.
Step 1: Divide 1224 by 972
Dividing 1224 by 972 gives us a quotient of 1 and a remainder of 252.
Step 2: Divide 972 by 252
Dividing 972 by 252 gives us a quotient of 3 and a remainder of 216.
Step 3: Divide 252 by 216
Dividing 252 by 216 gives us a quotient of 1 and a remainder of 36.
Step 4: Divide 216 by 36
Dividing 216 by 36 gives us a quotient of 6 and no remainder.
Therefore, the largest common divisor of 1224 and 972 is 36.
So, the greatest number that when divided into 1250 and 1000 leaves a remainder of 26 and 28 respectively is 36.
To find the greatest number that satisfies the given conditions, we can use the concept of the greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
Let's solve the problem step by step:
1. Subtract the remainders from their respective numbers:
- For 1250, the number 26 should be subtracted.
- For 1000, the number 28 should be subtracted.
After subtracting, we have:
- 1250 - 26 = 1224
- 1000 - 28 = 972
2. Calculate the GCD of the resulting numbers.
The GCD of 1224 and 972 is the greatest number that evenly divides both of them without leaving a remainder.
- The prime factorization of 1224 is 2^3 * 3 * 17.
- The prime factorization of 972 is 2^2 * 3^5.
To find the GCD, we take the highest power of each common prime factor:
- The common prime factors are 2 and 3.
- The highest power of 2 is 2^2 = 4.
- The highest power of 3 is 3.
Therefore, the GCD of 1224 and 972 is 4 * 3 = 12.
So, the greatest number that, when divided into 1250 and 1000, leaves remainders of 26 and 28 respectively, is 12.
I hope this explanation helps you understand how to find the solution.