Highest Common Factor of 555, 777, 906 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 555, 777, 906 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 555, 777, 906 is 3 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 555, 777, 906 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 555, 777, 906 is 3.
HCF(555, 777, 906) = 3
HCF of 555, 777, 906 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 555, 777, 906 is 3.
Highest Common Factor of 555,777,906 is 3
Step 1: Since 777 > 555, we apply the division lemma to 777 and 555, to get
777 = 555 x 1 + 222
Step 2: Since the reminder 555 ≠ 0, we apply division lemma to 222 and 555, to get
555 = 222 x 2 + 111
Step 3: We consider the new divisor 222 and the new remainder 111, and apply the division lemma to get
222 = 111 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 111, the HCF of 555 and 777 is 111
Notice that 111 = HCF(222,111) = HCF(555,222) = HCF(777,555) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 906 > 111, we apply the division lemma to 906 and 111, to get
906 = 111 x 8 + 18
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 18 and 111, to get
111 = 18 x 6 + 3
Step 3: We consider the new divisor 18 and the new remainder 3, and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 111 and 906 is 3
Notice that 3 = HCF(18,3) = HCF(111,18) = HCF(906,111) .
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Frequently Asked Questions on HCF of 555, 777, 906 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 555, 777, 906?
Answer: HCF of 555, 777, 906 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 555, 777, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 555, 777, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
