Highest Common Factor of 237, 916 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 237, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 237, 916 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 237, 916 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 237, 916 is 1.
HCF(237, 916) = 1
HCF of 237, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 237, 916 is 1.
Highest Common Factor of 237,916 is 1
Step 1: Since 916 > 237, we apply the division lemma to 916 and 237, to get
916 = 237 x 3 + 205
Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 205 and 237, to get
237 = 205 x 1 + 32
Step 3: We consider the new divisor 205 and the new remainder 32, and apply the division lemma to get
205 = 32 x 6 + 13
We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get
32 = 13 x 2 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 237 and 916 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(205,32) = HCF(237,205) = HCF(916,237) .
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Frequently Asked Questions on HCF of 237, 916 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 237, 916?
Answer: HCF of 237, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 237, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 237, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.