Highest Common Factor of 698, 967, 107 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 698, 967, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 698, 967, 107 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 698, 967, 107 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 698, 967, 107 is 1.
HCF(698, 967, 107) = 1
HCF of 698, 967, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 698, 967, 107 is 1.
Highest Common Factor of 698,967,107 is 1
Step 1: Since 967 > 698, we apply the division lemma to 967 and 698, to get
967 = 698 x 1 + 269
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 269 and 698, to get
698 = 269 x 2 + 160
Step 3: We consider the new divisor 269 and the new remainder 160, and apply the division lemma to get
269 = 160 x 1 + 109
We consider the new divisor 160 and the new remainder 109,and apply the division lemma to get
160 = 109 x 1 + 51
We consider the new divisor 109 and the new remainder 51,and apply the division lemma to get
109 = 51 x 2 + 7
We consider the new divisor 51 and the new remainder 7,and apply the division lemma to get
51 = 7 x 7 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 698 and 967 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(51,7) = HCF(109,51) = HCF(160,109) = HCF(269,160) = HCF(698,269) = HCF(967,698) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 1, we apply the division lemma to 107 and 1, to get
107 = 1 x 107 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 107 is 1
Notice that 1 = HCF(107,1) .
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Frequently Asked Questions on HCF of 698, 967, 107 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 698, 967, 107?
Answer: HCF of 698, 967, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 698, 967, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 698, 967, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.