Highest Common Factor of 876, 748, 645 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 876, 748, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 876, 748, 645 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 876, 748, 645 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 876, 748, 645 is 1.
HCF(876, 748, 645) = 1
HCF of 876, 748, 645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 876, 748, 645 is 1.
Highest Common Factor of 876,748,645 is 1
Step 1: Since 876 > 748, we apply the division lemma to 876 and 748, to get
876 = 748 x 1 + 128
Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 128 and 748, to get
748 = 128 x 5 + 108
Step 3: We consider the new divisor 128 and the new remainder 108, and apply the division lemma to get
128 = 108 x 1 + 20
We consider the new divisor 108 and the new remainder 20,and apply the division lemma to get
108 = 20 x 5 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 876 and 748 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(108,20) = HCF(128,108) = HCF(748,128) = HCF(876,748) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 645 > 4, we apply the division lemma to 645 and 4, to get
645 = 4 x 161 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 645 is 1
Notice that 1 = HCF(4,1) = HCF(645,4) .
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Frequently Asked Questions on HCF of 876, 748, 645 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 876, 748, 645?
Answer: HCF of 876, 748, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 876, 748, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 876, 748, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.