Highest Common Factor of 76, 105 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 76, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 76, 105 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 76, 105 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 76, 105 is 1.
HCF(76, 105) = 1
HCF of 76, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 76, 105 is 1.
Highest Common Factor of 76,105 is 1
Step 1: Since 105 > 76, we apply the division lemma to 105 and 76, to get
105 = 76 x 1 + 29
Step 2: Since the reminder 76 ≠ 0, we apply division lemma to 29 and 76, to get
76 = 29 x 2 + 18
Step 3: We consider the new divisor 29 and the new remainder 18, and apply the division lemma to get
29 = 18 x 1 + 11
We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 76 and 105 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(29,18) = HCF(76,29) = HCF(105,76) .
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Frequently Asked Questions on HCF of 76, 105 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 76, 105?
Answer: HCF of 76, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 76, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 76, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.