Highest Common Factor of 1356, 2101 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 1356, 2101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1356, 2101 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 1356, 2101 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 1356, 2101 is 1.
HCF(1356, 2101) = 1
HCF of 1356, 2101 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1356, 2101 is 1.
Highest Common Factor of 1356,2101 is 1
Step 1: Since 2101 > 1356, we apply the division lemma to 2101 and 1356, to get
2101 = 1356 x 1 + 745
Step 2: Since the reminder 1356 ≠ 0, we apply division lemma to 745 and 1356, to get
1356 = 745 x 1 + 611
Step 3: We consider the new divisor 745 and the new remainder 611, and apply the division lemma to get
745 = 611 x 1 + 134
We consider the new divisor 611 and the new remainder 134,and apply the division lemma to get
611 = 134 x 4 + 75
We consider the new divisor 134 and the new remainder 75,and apply the division lemma to get
134 = 75 x 1 + 59
We consider the new divisor 75 and the new remainder 59,and apply the division lemma to get
75 = 59 x 1 + 16
We consider the new divisor 59 and the new remainder 16,and apply the division lemma to get
59 = 16 x 3 + 11
We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1356 and 2101 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(59,16) = HCF(75,59) = HCF(134,75) = HCF(611,134) = HCF(745,611) = HCF(1356,745) = HCF(2101,1356) .
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Frequently Asked Questions on HCF of 1356, 2101 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 1356, 2101?
Answer: HCF of 1356, 2101 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1356, 2101 using Euclid's Algorithm?
Answer: For arbitrary numbers 1356, 2101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.