Highest Common Factor of 912, 1708 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 912, 1708 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 1708 is 4 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 912, 1708 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 912, 1708 is 4.
HCF(912, 1708) = 4
HCF of 912, 1708 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 1708 is 4.
Highest Common Factor of 912,1708 is 4
Step 1: Since 1708 > 912, we apply the division lemma to 1708 and 912, to get
1708 = 912 x 1 + 796
Step 2: Since the reminder 912 ≠ 0, we apply division lemma to 796 and 912, to get
912 = 796 x 1 + 116
Step 3: We consider the new divisor 796 and the new remainder 116, and apply the division lemma to get
796 = 116 x 6 + 100
We consider the new divisor 116 and the new remainder 100,and apply the division lemma to get
116 = 100 x 1 + 16
We consider the new divisor 100 and the new remainder 16,and apply the division lemma to get
100 = 16 x 6 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 912 and 1708 is 4
Notice that 4 = HCF(16,4) = HCF(100,16) = HCF(116,100) = HCF(796,116) = HCF(912,796) = HCF(1708,912) .
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Frequently Asked Questions on HCF of 912, 1708 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 912, 1708?
Answer: HCF of 912, 1708 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 1708 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 1708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.