Question : Which of the following numbers leaves the remainder equal to the highest common factor of 6, 8, and 9, when divided by 6, 8 and 9?
Option 1: 291
Option 2: 575
Option 3: 506
Option 4: 433
Correct Answer: 433
Solution :
The highest common factor (HCF) of 6, 8, and 9 is 1
For 291:
Remainder when divided by 6: 291 mod 6 = 3
Remainder when divided by 8: 291 mod 8 = 3
Remainder when divided by 9: 291 mod 9 = 0
It doesn't satisfy the condition for the highest common factor.
For 575:
Remainder when divided by 6: 575 mod 6 = 5
Remainder when divided by 8: 575 mod 8 = 7
Remainder when divided by 9: 575 mod 9 = 2
It doesn't satisfy the condition for the highest common factor.
For 506:
Remainder when divided by 6: 506 mod 6 = 2
Remainder when divided by 8: 506 mod 8 = 2
Remainder when divided by 9: 506 mod 9 = 7
It doesn't satisfy the condition for the highest common factor.
For 433:
Remainder when divided by 6: 433 mod 6 = 1
Remainder when divided by 8: 433 mod 8 = 1
Remainder when divided by 9: 433 mod 9 = 1
It satisfies the condition for the highest common factor.
Hence, the correct answer is 433.
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