Find the largest number which divides 438 and 606, leaving remainder 6

1.	Find the largest number which divides 438 and 606, leaving remainder 6 in each case.
Answer» Largest number which divides 438 and 606, leaving remainder 6 in each case is actually the largest number which divide 432 (438 – 6) and 600 (606 – 6). The largest number which divides 432 and 600 is HCF (432, 600). Now, write 432 and 600 into prime factorization form, 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁴ × 3³ . 600 = 6 × 10² = 2× 3 × 2 × 5 × 2 × 5 = 2³ × 3 × 5² . HCF (432, 600) = product of smallest power of each common factor in the prime factorization of numbers = 2³ × 3 = 8 × 3 = 24. Thus, the largest number which divides 438 and 606, leaving remainder 6 is 24.

Find the largest number which divides 438 and 606, leaving remainder 6 in each case.

Answer»

Largest number which divides 438 and 606, leaving remainder 6 in each case is actually

the largest number which divide 432 (438 – 6) and 600 (606 – 6).

The largest number which divides 432 and 600 is HCF (432, 600).

Now, write 432 and 600 into prime factorization form,

432 = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁴ × 3³ .

600 = 6 × 10² = 2× 3 × 2 × 5 × 2 × 5 = 2³ × 3 × 5² .

HCF (432, 600) = product of smallest power of each common factor in the prime

factorization of numbers = 2³ × 3 = 8 × 3 = 24.

Thus, the largest number which divides 438 and 606, leaving remainder 6 is 24.

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