Highest Common Factor of 1878, 1104 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 1878, 1104 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 1878, 1104 is 6 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 1878, 1104 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 1878, 1104 is 6.
HCF(1878, 1104) = 6
HCF of 1878, 1104 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1878, 1104 is 6.
Highest Common Factor of 1878,1104 is 6
Step 1: Since 1878 > 1104, we apply the division lemma to 1878 and 1104, to get
1878 = 1104 x 1 + 774
Step 2: Since the reminder 1104 ≠ 0, we apply division lemma to 774 and 1104, to get
1104 = 774 x 1 + 330
Step 3: We consider the new divisor 774 and the new remainder 330, and apply the division lemma to get
774 = 330 x 2 + 114
We consider the new divisor 330 and the new remainder 114,and apply the division lemma to get
330 = 114 x 2 + 102
We consider the new divisor 114 and the new remainder 102,and apply the division lemma to get
114 = 102 x 1 + 12
We consider the new divisor 102 and the new remainder 12,and apply the division lemma to get
102 = 12 x 8 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1878 and 1104 is 6
Notice that 6 = HCF(12,6) = HCF(102,12) = HCF(114,102) = HCF(330,114) = HCF(774,330) = HCF(1104,774) = HCF(1878,1104) .
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Frequently Asked Questions on HCF of 1878, 1104 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 1878, 1104?
Answer: HCF of 1878, 1104 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1878, 1104 using Euclid's Algorithm?
Answer: For arbitrary numbers 1878, 1104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.