Highest Common Factor of 706, 900 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 706, 900 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 900 is 2 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 706, 900 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 706, 900 is 2.
HCF(706, 900) = 2
HCF of 706, 900 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 706, 900 is 2.
Highest Common Factor of 706,900 is 2
Step 1: Since 900 > 706, we apply the division lemma to 900 and 706, to get
900 = 706 x 1 + 194
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 194 and 706, to get
706 = 194 x 3 + 124
Step 3: We consider the new divisor 194 and the new remainder 124, and apply the division lemma to get
194 = 124 x 1 + 70
We consider the new divisor 124 and the new remainder 70,and apply the division lemma to get
124 = 70 x 1 + 54
We consider the new divisor 70 and the new remainder 54,and apply the division lemma to get
70 = 54 x 1 + 16
We consider the new divisor 54 and the new remainder 16,and apply the division lemma to get
54 = 16 x 3 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 706 and 900 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(54,16) = HCF(70,54) = HCF(124,70) = HCF(194,124) = HCF(706,194) = HCF(900,706) .
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Frequently Asked Questions on HCF of 706, 900 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 706, 900?
Answer: HCF of 706, 900 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 900 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
