Highest Common Factor of 109, 491, 274, 735 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 109, 491, 274, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 109, 491, 274, 735 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 109, 491, 274, 735 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 109, 491, 274, 735 is 1.
HCF(109, 491, 274, 735) = 1
HCF of 109, 491, 274, 735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 109, 491, 274, 735 is 1.
Highest Common Factor of 109,491,274,735 is 1
Step 1: Since 491 > 109, we apply the division lemma to 491 and 109, to get
491 = 109 x 4 + 55
Step 2: Since the reminder 109 ≠ 0, we apply division lemma to 55 and 109, to get
109 = 55 x 1 + 54
Step 3: We consider the new divisor 55 and the new remainder 54, and apply the division lemma to get
55 = 54 x 1 + 1
We consider the new divisor 54 and the new remainder 1, and apply the division lemma to get
54 = 1 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 109 and 491 is 1
Notice that 1 = HCF(54,1) = HCF(55,54) = HCF(109,55) = HCF(491,109) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 274 > 1, we apply the division lemma to 274 and 1, to get
274 = 1 x 274 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 274 is 1
Notice that 1 = HCF(274,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get
735 = 1 x 735 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1
Notice that 1 = HCF(735,1) .
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Frequently Asked Questions on HCF of 109, 491, 274, 735 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 109, 491, 274, 735?
Answer: HCF of 109, 491, 274, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 109, 491, 274, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 109, 491, 274, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.