Highest Common Factor of 291, 21688 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 291, 21688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 291, 21688 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 291, 21688 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 291, 21688 is 1.
HCF(291, 21688) = 1
HCF of 291, 21688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 291, 21688 is 1.
Highest Common Factor of 291,21688 is 1
Step 1: Since 21688 > 291, we apply the division lemma to 21688 and 291, to get
21688 = 291 x 74 + 154
Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 154 and 291, to get
291 = 154 x 1 + 137
Step 3: We consider the new divisor 154 and the new remainder 137, and apply the division lemma to get
154 = 137 x 1 + 17
We consider the new divisor 137 and the new remainder 17,and apply the division lemma to get
137 = 17 x 8 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 291 and 21688 is 1
Notice that 1 = HCF(17,1) = HCF(137,17) = HCF(154,137) = HCF(291,154) = HCF(21688,291) .
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Frequently Asked Questions on HCF of 291, 21688 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 291, 21688?
Answer: HCF of 291, 21688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 291, 21688 using Euclid's Algorithm?
Answer: For arbitrary numbers 291, 21688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.