Highest Common Factor of 90, 495, 460, 657 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 90, 495, 460, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 90, 495, 460, 657 is 1 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 90, 495, 460, 657 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 90, 495, 460, 657 is 1.
HCF(90, 495, 460, 657) = 1
HCF of 90, 495, 460, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 90, 495, 460, 657 is 1.
Highest Common Factor of 90,495,460,657 is 1
Step 1: Since 495 > 90, we apply the division lemma to 495 and 90, to get
495 = 90 x 5 + 45
Step 2: Since the reminder 90 ≠ 0, we apply division lemma to 45 and 90, to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 90 and 495 is 45
Notice that 45 = HCF(90,45) = HCF(495,90) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 45, we apply the division lemma to 460 and 45, to get
460 = 45 x 10 + 10
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 10 and 45, to get
45 = 10 x 4 + 5
Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma 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 45 and 460 is 5
Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(460,45) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 5, we apply the division lemma to 657 and 5, to get
657 = 5 x 131 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 657 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(657,5) .
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Frequently Asked Questions on HCF of 90, 495, 460, 657 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 90, 495, 460, 657?
Answer: HCF of 90, 495, 460, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 90, 495, 460, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 90, 495, 460, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.