Highest Common Factor of 605, 1100 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 605, 1100 i.e. 55 the largest integer that leaves a remainder zero for all numbers.
HCF of 605, 1100 is 55 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 605, 1100 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 605, 1100 is 55.
HCF(605, 1100) = 55
HCF of 605, 1100 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 605, 1100 is 55.
Highest Common Factor of 605,1100 is 55
Step 1: Since 1100 > 605, we apply the division lemma to 1100 and 605, to get
1100 = 605 x 1 + 495
Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 495 and 605, to get
605 = 495 x 1 + 110
Step 3: We consider the new divisor 495 and the new remainder 110, and apply the division lemma to get
495 = 110 x 4 + 55
We consider the new divisor 110 and the new remainder 55, and apply the division lemma to get
110 = 55 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 605 and 1100 is 55
Notice that 55 = HCF(110,55) = HCF(495,110) = HCF(605,495) = HCF(1100,605) .
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Frequently Asked Questions on HCF of 605, 1100 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 605, 1100?
Answer: HCF of 605, 1100 is 55 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 605, 1100 using Euclid's Algorithm?
Answer: For arbitrary numbers 605, 1100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.