Highest Common Factor of 841, 354 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 841, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 841, 354 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 841, 354 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 841, 354 is 1.
HCF(841, 354) = 1
HCF of 841, 354 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 841, 354 is 1.
Highest Common Factor of 841,354 is 1
Step 1: Since 841 > 354, we apply the division lemma to 841 and 354, to get
841 = 354 x 2 + 133
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 133 and 354, to get
354 = 133 x 2 + 88
Step 3: We consider the new divisor 133 and the new remainder 88, and apply the division lemma to get
133 = 88 x 1 + 45
We consider the new divisor 88 and the new remainder 45,and apply the division lemma to get
88 = 45 x 1 + 43
We consider the new divisor 45 and the new remainder 43,and apply the division lemma to get
45 = 43 x 1 + 2
We consider the new divisor 43 and the new remainder 2,and apply the division lemma to get
43 = 2 x 21 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 841 and 354 is 1
Notice that 1 = HCF(2,1) = HCF(43,2) = HCF(45,43) = HCF(88,45) = HCF(133,88) = HCF(354,133) = HCF(841,354) .
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Frequently Asked Questions on HCF of 841, 354 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 841, 354?
Answer: HCF of 841, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 841, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 841, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.