Highest Common Factor of 497, 854 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 497, 854 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 497, 854 is 7 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 497, 854 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 497, 854 is 7.
HCF(497, 854) = 7
HCF of 497, 854 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 497, 854 is 7.
Highest Common Factor of 497,854 is 7
Step 1: Since 854 > 497, we apply the division lemma to 854 and 497, to get
854 = 497 x 1 + 357
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 357 and 497, to get
497 = 357 x 1 + 140
Step 3: We consider the new divisor 357 and the new remainder 140, and apply the division lemma to get
357 = 140 x 2 + 77
We consider the new divisor 140 and the new remainder 77,and apply the division lemma to get
140 = 77 x 1 + 63
We consider the new divisor 77 and the new remainder 63,and apply the division lemma to get
77 = 63 x 1 + 14
We consider the new divisor 63 and the new remainder 14,and apply the division lemma to get
63 = 14 x 4 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 497 and 854 is 7
Notice that 7 = HCF(14,7) = HCF(63,14) = HCF(77,63) = HCF(140,77) = HCF(357,140) = HCF(497,357) = HCF(854,497) .
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Frequently Asked Questions on HCF of 497, 854 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 497, 854?
Answer: HCF of 497, 854 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 497, 854 using Euclid's Algorithm?
Answer: For arbitrary numbers 497, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.