Highest Common Factor of 690, 880, 495 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 690, 880, 495 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 880, 495 is 5 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 690, 880, 495 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 690, 880, 495 is 5.
HCF(690, 880, 495) = 5
HCF of 690, 880, 495 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 690, 880, 495 is 5.
Highest Common Factor of 690,880,495 is 5
Step 1: Since 880 > 690, we apply the division lemma to 880 and 690, to get
880 = 690 x 1 + 190
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 190 and 690, to get
690 = 190 x 3 + 120
Step 3: We consider the new divisor 190 and the new remainder 120, and apply the division lemma to get
190 = 120 x 1 + 70
We consider the new divisor 120 and the new remainder 70,and apply the division lemma to get
120 = 70 x 1 + 50
We consider the new divisor 70 and the new remainder 50,and apply the division lemma to get
70 = 50 x 1 + 20
We consider the new divisor 50 and the new remainder 20,and apply the division lemma to get
50 = 20 x 2 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 690 and 880 is 10
Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(70,50) = HCF(120,70) = HCF(190,120) = HCF(690,190) = HCF(880,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 495 > 10, we apply the division lemma to 495 and 10, to get
495 = 10 x 49 + 5
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 5 and 10, to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 10 and 495 is 5
Notice that 5 = HCF(10,5) = HCF(495,10) .
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Frequently Asked Questions on HCF of 690, 880, 495 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 690, 880, 495?
Answer: HCF of 690, 880, 495 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 880, 495 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 880, 495 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.