Highest Common Factor of 105, 689, 948 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, 689, 948 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 689, 948 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, 689, 948 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, 689, 948 is 1.
HCF(105, 689, 948) = 1
HCF of 105, 689, 948 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, 689, 948 is 1.
Highest Common Factor of 105,689,948 is 1
Step 1: Since 689 > 105, we apply the division lemma to 689 and 105, to get
689 = 105 x 6 + 59
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 59 and 105, to get
105 = 59 x 1 + 46
Step 3: We consider the new divisor 59 and the new remainder 46, and apply the division lemma to get
59 = 46 x 1 + 13
We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get
46 = 13 x 3 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 105 and 689 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(59,46) = HCF(105,59) = HCF(689,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 948 > 1, we apply the division lemma to 948 and 1, to get
948 = 1 x 948 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 948 is 1
Notice that 1 = HCF(948,1) .
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Frequently Asked Questions on HCF of 105, 689, 948 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, 689, 948?
Answer: HCF of 105, 689, 948 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 689, 948 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 689, 948 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.