Highest Common Factor of 170, 629, 373, 691 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 170, 629, 373, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 629, 373, 691 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 170, 629, 373, 691 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 170, 629, 373, 691 is 1.
HCF(170, 629, 373, 691) = 1
HCF of 170, 629, 373, 691 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 629, 373, 691 is 1.
Highest Common Factor of 170,629,373,691 is 1
Step 1: Since 629 > 170, we apply the division lemma to 629 and 170, to get
629 = 170 x 3 + 119
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 119 and 170, to get
170 = 119 x 1 + 51
Step 3: We consider the new divisor 119 and the new remainder 51, and apply the division lemma to get
119 = 51 x 2 + 17
We consider the new divisor 51 and the new remainder 17, and apply the division lemma to get
51 = 17 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 170 and 629 is 17
Notice that 17 = HCF(51,17) = HCF(119,51) = HCF(170,119) = HCF(629,170) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 373 > 17, we apply the division lemma to 373 and 17, to get
373 = 17 x 21 + 16
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 16 and 17, to get
17 = 16 x 1 + 1
Step 3: We consider the new divisor 16 and the new remainder 1, and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 373 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(373,17) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 691 > 1, we apply the division lemma to 691 and 1, to get
691 = 1 x 691 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 691 is 1
Notice that 1 = HCF(691,1) .
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Frequently Asked Questions on HCF of 170, 629, 373, 691 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 170, 629, 373, 691?
Answer: HCF of 170, 629, 373, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 629, 373, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 629, 373, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.