Find the greatest number that will divide 445 572 and 699
Answers
Answer: 3
Step-by-step explanation:
The factors of 699 are: 1, 3, 233, 699
The factors of 445572 are: 1, 2, 3, 4, 6, 9, 12, 18, 36, 12377, 24754, 37131, 49508, 74262, 111393, 148524, 222786, 445572
Then the greatest common factor is 3
The required number when divides 445, 572 and 699 leaves remainders 4, 5 and 6.
This means:
445 – 4 = 441, 572 – 5 = 561 and 699 – 6 = 693 are completely divisible by the number.
∴ The required number = HCF of 441, 567 and 693.
First consider 441 and 567,
By applying Euclid’s division lemma
567 = 441 × 1 + 126
441 = 126 × 3 + 63
126 = 63 × 2 + 0
∴ HCF of 441 and 567 = 63
Now consider 63 and 693
By applying Euclid’s division lemma
693 = 63 × 11 + 0
∴ HCF of 441, 567 and 693 = 63
Hence required number is 63.
Hope this helps