Highest Common Factor of 545, 974, 215 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 545, 974, 215 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 545, 974, 215 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 545, 974, 215 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 545, 974, 215 is 1.
HCF(545, 974, 215) = 1
HCF of 545, 974, 215 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 545, 974, 215 is 1.
Highest Common Factor of 545,974,215 is 1
Step 1: Since 974 > 545, we apply the division lemma to 974 and 545, to get
974 = 545 x 1 + 429
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 429 and 545, to get
545 = 429 x 1 + 116
Step 3: We consider the new divisor 429 and the new remainder 116, and apply the division lemma to get
429 = 116 x 3 + 81
We consider the new divisor 116 and the new remainder 81,and apply the division lemma to get
116 = 81 x 1 + 35
We consider the new divisor 81 and the new remainder 35,and apply the division lemma to get
81 = 35 x 2 + 11
We consider the new divisor 35 and the new remainder 11,and apply the division lemma to get
35 = 11 x 3 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 1
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 545 and 974 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(81,35) = HCF(116,81) = HCF(429,116) = HCF(545,429) = HCF(974,545) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 215 > 1, we apply the division lemma to 215 and 1, to get
215 = 1 x 215 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 215 is 1
Notice that 1 = HCF(215,1) .
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Frequently Asked Questions on HCF of 545, 974, 215 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 545, 974, 215?
Answer: HCF of 545, 974, 215 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 545, 974, 215 using Euclid's Algorithm?
Answer: For arbitrary numbers 545, 974, 215 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
