Highest Common Factor of 658, 992 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 658, 992 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 992 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 658, 992 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 658, 992 is 2.
HCF(658, 992) = 2
HCF of 658, 992 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 658, 992 is 2.
Highest Common Factor of 658,992 is 2
Step 1: Since 992 > 658, we apply the division lemma to 992 and 658, to get
992 = 658 x 1 + 334
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 334 and 658, to get
658 = 334 x 1 + 324
Step 3: We consider the new divisor 334 and the new remainder 324, and apply the division lemma to get
334 = 324 x 1 + 10
We consider the new divisor 324 and the new remainder 10,and apply the division lemma to get
324 = 10 x 32 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 658 and 992 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(324,10) = HCF(334,324) = HCF(658,334) = HCF(992,658) .
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Frequently Asked Questions on HCF of 658, 992 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 658, 992?
Answer: HCF of 658, 992 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 992 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.