Highest Common Factor of 258, 688, 924 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 258, 688, 924 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 258, 688, 924 is 2 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 258, 688, 924 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 258, 688, 924 is 2.
HCF(258, 688, 924) = 2
HCF of 258, 688, 924 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 258, 688, 924 is 2.
Highest Common Factor of 258,688,924 is 2
Step 1: Since 688 > 258, we apply the division lemma to 688 and 258, to get
688 = 258 x 2 + 172
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 172 and 258, to get
258 = 172 x 1 + 86
Step 3: We consider the new divisor 172 and the new remainder 86, and apply the division lemma to get
172 = 86 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 86, the HCF of 258 and 688 is 86
Notice that 86 = HCF(172,86) = HCF(258,172) = HCF(688,258) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 924 > 86, we apply the division lemma to 924 and 86, to get
924 = 86 x 10 + 64
Step 2: Since the reminder 86 ≠ 0, we apply division lemma to 64 and 86, to get
86 = 64 x 1 + 22
Step 3: We consider the new divisor 64 and the new remainder 22, and apply the division lemma to get
64 = 22 x 2 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 86 and 924 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(64,22) = HCF(86,64) = HCF(924,86) .
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Frequently Asked Questions on HCF of 258, 688, 924 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 258, 688, 924?
Answer: HCF of 258, 688, 924 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 258, 688, 924 using Euclid's Algorithm?
Answer: For arbitrary numbers 258, 688, 924 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
