Highest Common Factor of 105, 175, 981 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 105, 175, 981 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 175, 981 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 105, 175, 981 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 105, 175, 981 is 1.
HCF(105, 175, 981) = 1
HCF of 105, 175, 981 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 175, 981 is 1.
Highest Common Factor of 105,175,981 is 1
Step 1: Since 175 > 105, we apply the division lemma to 175 and 105, to get
175 = 105 x 1 + 70
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 70 and 105, to get
105 = 70 x 1 + 35
Step 3: We consider the new divisor 70 and the new remainder 35, and apply the division lemma to get
70 = 35 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 105 and 175 is 35
Notice that 35 = HCF(70,35) = HCF(105,70) = HCF(175,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 981 > 35, we apply the division lemma to 981 and 35, to get
981 = 35 x 28 + 1
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 1 and 35, to get
35 = 1 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 35 and 981 is 1
Notice that 1 = HCF(35,1) = HCF(981,35) .
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Frequently Asked Questions on HCF of 105, 175, 981 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 105, 175, 981?
Answer: HCF of 105, 175, 981 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 175, 981 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 175, 981 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.