Highest Common Factor of 4100, 1221 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 4100, 1221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4100, 1221 is 1 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 4100, 1221 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 4100, 1221 is 1.
HCF(4100, 1221) = 1
HCF of 4100, 1221 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4100, 1221 is 1.
Highest Common Factor of 4100,1221 is 1
Step 1: Since 4100 > 1221, we apply the division lemma to 4100 and 1221, to get
4100 = 1221 x 3 + 437
Step 2: Since the reminder 1221 ≠ 0, we apply division lemma to 437 and 1221, to get
1221 = 437 x 2 + 347
Step 3: We consider the new divisor 437 and the new remainder 347, and apply the division lemma to get
437 = 347 x 1 + 90
We consider the new divisor 347 and the new remainder 90,and apply the division lemma to get
347 = 90 x 3 + 77
We consider the new divisor 90 and the new remainder 77,and apply the division lemma to get
90 = 77 x 1 + 13
We consider the new divisor 77 and the new remainder 13,and apply the division lemma to get
77 = 13 x 5 + 12
We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4100 and 1221 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(77,13) = HCF(90,77) = HCF(347,90) = HCF(437,347) = HCF(1221,437) = HCF(4100,1221) .
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Frequently Asked Questions on HCF of 4100, 1221 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 4100, 1221?
Answer: HCF of 4100, 1221 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4100, 1221 using Euclid's Algorithm?
Answer: For arbitrary numbers 4100, 1221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.