Question

The greatest number, which divides 1477 and 671 to leave 0 and 6 respectively as remainders, is:

• A. 17
• B. 16
• C. 20
• D. 7

Answer 1

Answer:

D. 7

The greatest number that divides $1477$ and $671$ to leave remainders of $0$ and $6$ is $7$.

1. Subtract the remainders

First, subtract the respective remainders from the given numbers to find the numbers that are exactly divisible.

• For $1477$: $1477 - 0 = 1477$

• For $671$: $671 - 6 = 665$

2. Find prime factors

Next, find the prime factorization of both resulting numbers.

• For $1477$: $1477 = 7 \times 211$

• For $665$: $665 = 5 \times 7 \times 19$

3. Identify common factors

Now, look for the highest common factor ($\text{HCF}$) by identifying the common prime factors in both lists.

• Common factor: $7$

• $\text{HCF}(1477, 665) = 7$

Final Answer

The greatest number that divides $1477$ and $671$ leaving remainders $0$ and $6$ is $7$.