Highest Common Factor of 1971, 3357 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 1971, 3357 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 1971, 3357 is 9 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 1971, 3357 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 1971, 3357 is 9.
HCF(1971, 3357) = 9
HCF of 1971, 3357 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1971, 3357 is 9.
Highest Common Factor of 1971,3357 is 9
Step 1: Since 3357 > 1971, we apply the division lemma to 3357 and 1971, to get
3357 = 1971 x 1 + 1386
Step 2: Since the reminder 1971 ≠ 0, we apply division lemma to 1386 and 1971, to get
1971 = 1386 x 1 + 585
Step 3: We consider the new divisor 1386 and the new remainder 585, and apply the division lemma to get
1386 = 585 x 2 + 216
We consider the new divisor 585 and the new remainder 216,and apply the division lemma to get
585 = 216 x 2 + 153
We consider the new divisor 216 and the new remainder 153,and apply the division lemma to get
216 = 153 x 1 + 63
We consider the new divisor 153 and the new remainder 63,and apply the division lemma to get
153 = 63 x 2 + 27
We consider the new divisor 63 and the new remainder 27,and apply the division lemma to get
63 = 27 x 2 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 1971 and 3357 is 9
Notice that 9 = HCF(27,9) = HCF(63,27) = HCF(153,63) = HCF(216,153) = HCF(585,216) = HCF(1386,585) = HCF(1971,1386) = HCF(3357,1971) .
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Frequently Asked Questions on HCF of 1971, 3357 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 1971, 3357?
Answer: HCF of 1971, 3357 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1971, 3357 using Euclid's Algorithm?
Answer: For arbitrary numbers 1971, 3357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.