Question

Find the greatest number that will divide 148 and 246 leaving remainder 4 and 6 respectively.

Answer 1

To find the greatest number that will divide 148 and 246, leaving remainders of 4 and 6 respectively, you can use the concept of the greatest common divisor (GCD).

Let GCD(148, 246) = x be the greatest number you're looking for.

We know that 148 can be expressed as:

148 = 4k + 4 (where k is an integer)

Similarly, 246 can be expressed as:

246 = 4m + 6 (where m is an integer)

Now, we can simplify these equations:

k = (148 - 4) / 4 = 144 / 4 = 36

m = (246 - 6) / 4 = 240 / 4 = 60

So, 148 is 4 times 36 plus a remainder of 4, and 246 is 4 times 60 plus a remainder of 6.

Now, find the GCD of 148 and 246:

GCD(148, 246) = GCD(4k + 4, 4m + 6)

Since the remainders are 4 and 6, respectively, the greatest number that divides both 148 and 246 leaving those remainders is the GCD of 4 and 6.

GCD(4, 6) = 2

Therefore, the greatest number that will divide 148 and 246, leaving remainders of 4 and 6 respectively, is 2.

Answer 2

To solve this problem, we can use the concept of the common factor (HCF) or the greatest common factor (GCF). 

Let's start by finding the factors of 148 and 246:

Factors of 148: 1, 2, 4, 37, 74, 148

Factors of 246: 1, 2, 3, 6, 41, 82, 123, 246

Next, let's identify the numbers that leave a remainder of 4 when dividing 148 and a remainder of 6 when dividing 246:

Numbers leaving remainder 4 when dividing 148: 4, 37, 74, 148

Numbers leaving remainder 6 when dividing 246: 6, 82, 246

The greatest number that is common to both lists is 246 (which leaves a remainder of 6 when dividing 246). 

Therefore, the greatest number that will divide 148 and 246, leaving a remainder of 4 and 6 respectively, is 246.

Answer 3

To find the greatest number that will divide 148 and 246, leaving remainders of 4 and 6 respectively, you can use the concept of the greatest common divisor (GCD).

Let GCD(a, b) represent the greatest common divisor of two numbers a and b.

So, in this case, we have:

GCD(148 - 4, 246 - 6)

GCD(144, 240)

Now, let's find the GCD of 144 and 240.

Divide 240 by 144:

240 = 1 * 144 + 96

Now, divide 144 by 96:

144 = 1 * 96 + 48

Continuing this process:

96 = 2 * 48 + 0

Since we've reached a remainder of 0, the greatest common divisor of 144 and 240 is the last non-zero remainder, which is 48.

So, the greatest number that will divide 148 and 246, leaving remainders of 4 and 6 respectively, is 48.

Answer 4

The greatest number that satisfies the given conditions is 2.

The greatest number that can divide both 148 and 246, leaving remainders of 4 and 6 respectively, is the greatest common divisor (GCD) of the two numbers. In this case, the GCD is 2. The GCD is the largest positive integer that divides both numbers without leaving a remainder.

Answer 5

Let's call the greatest number that divides 148 and 246 and leaves remainders of 4 and 6, respectively, as "n".

This means that there exist integers "a" and "b" such that:

148 = an + 4 246 = bn + 6

We can rewrite these equations as:

an = 148 - 4 = 144 bn = 246 - 6 = 240

To find the greatest common divisor (GCD) of 144 and 240, we can use the Euclidean algorithm:

240 = 1 * 144 + 96 144 = 1 * 96 + 48 96 = 2 * 48 + 0

Therefore, the GCD of 144 and 240 is 48.

Since n divides both 144 and 240, it must also divide their GCD, which is 48. Therefore, the greatest number that will divide 148 and 246 leaving remainders of 4 and 6, respectively, is n = 48.

Answer 6

Let's first calculate the GCD of 148 and 246. Then, we'll account for the remainders.

Find the GCD of 148 and 246:

You can use the Euclidean algorithm for this:

GCD(148, 246) = GCD(148, 246 - 1 * 148)

GCD(148, 246) = GCD(148, 98)

GCD(148, 98) = GCD(148 - 1 * 98, 98)

GCD(148, 98) = GCD(50, 98)

Now, continue:

GCD(50, 98) = GCD(50, 98 - 1 * 50)

GCD(50, 98) = GCD(50, 48)

GCD(50, 48) = GCD(50 - 1 * 48, 48)

GCD(50, 48) = GCD(2, 48)

Now, it's clear that the GCD is 2 because 2 is the largest number that divides both 2 and 48 without a remainder.

Now, consider the remainders:

If 148 is divided by 2 with a remainder of 4, it can be represented as 148 = 2k + 4, where k is the quotient.

Similarly, if 246 is divided by 2 with a remainder of 6, it can be represented as 246 = 2m + 6, where m is the quotient.

Now, if you subtract the first equation from the second equation:

(246 - 148) = (2m + 6) - (2k + 4)

98 = 2m - 2k

98 = 2(m - k)

Now, divide both sides by 2:

49 = m - k

This equation tells you that 49 is the difference between the two quotients (m and k). Since the GCD of 148 and 246 is 2, the greatest number that divides them with remainders of 4 and 6 is 2 * 49, which is equal to 98.

Answer 7

The greatest number that can divide both numbers is 48

148 /48 = 3 reminder 4

246/48 = 5 remainder 6

Subtract 4 from 148 and 6 from 246

148 - 4 = 144

246 - 6 = 240 

Use the greatest common divisor (GCD)

Then you will get 48

Answer 8

To find the greatest number that will divide 148 and 246, leaving remainders of 4 and 6 respectively, we can use the method of finding the highest common factor (HCF) or greatest common divisor (GCD).

First, let's subtract the respective remainders from 148 and 246:

For 148: \(148 - 4 = 144\)

For 246: \(246 - 6 = 240\)

Now, we need to find the HCF of 144 and 240:

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.

The common factors of 144 and 240 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor among them is 24.

Therefore, the greatest number that will divide 148 and 246, leaving remainders 4 and 6 respectively, is 24.