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Use Euclid's Division Algorithm to find the HCF of 4052 and 12576
Answers
Answer:
According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.
HCF is the largest number which exactly divides two or more positive integers.
Since 12576 > 4052
12576 = (4052 × 3) + 420
420 is a reminder which is not equal to zero (420 ≠ 0).
4052 = (420 × 9) + 272
271 is a reminder which is not equal to zero (272 ≠ 0).
Now consider the new divisor 272 and the new remainder 148.
272 = (148 × 1) + 124
Now consider the new divisor 148 and the new remainder 124.
148 = (124 × 1) + 24
Now consider the new divisor 124 and the new remainder 24.
124 = (24 × 5) + 4
Now consider the new divisor 24 and the new remainder 4.
24 = (4 × 6) + 0
Reminder = 0
Divisor = 4
HCF of 12576 and 4052 = 4.
HCF of 4052 and 12576
add
HCF of 4052 and 12576 is the largest possible number that divides 4052 and 12576 exactly without any remainder. The factors of 4052 and 12576 are 1, 2, 4, 1013, 2026, 4052 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 131, 262, 393, 524, 786, 1048, 1572, 2096, 3144, 4192, 6288, 12576 respectively. There are 3 commonly used methods to find the HCF of 4052 and 12576 - Euclidean algorithm, long division, and prime factorization.
What is HCF of 4052 and 12576?
Answer: HCF of 4052 and 12576 is 4.
HCF of 4052 and 12576
Explanation:
The HCF of two non-zero integers, x(4052) and y(12576), is the highest positive integer m(4) that divides both x(4052) and y(12576) without any remainder.
Methods to Find HCF of 4052 and 12576
Let's look at the different methods for finding the HCF of 4052 and 12576.
Long Division Method
Prime Factorization Method
Listing Common Factors