Highest Common Factor of 506, 690, 153 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 506, 690, 153 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 690, 153 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 506, 690, 153 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 506, 690, 153 is 1.
HCF(506, 690, 153) = 1
HCF of 506, 690, 153 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 690, 153 is 1.
Highest Common Factor of 506,690,153 is 1
Step 1: Since 690 > 506, we apply the division lemma to 690 and 506, to get
690 = 506 x 1 + 184
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 184 and 506, to get
506 = 184 x 2 + 138
Step 3: We consider the new divisor 184 and the new remainder 138, and apply the division lemma to get
184 = 138 x 1 + 46
We consider the new divisor 138 and the new remainder 46, and apply the division lemma to get
138 = 46 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 46, the HCF of 506 and 690 is 46
Notice that 46 = HCF(138,46) = HCF(184,138) = HCF(506,184) = HCF(690,506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 153 > 46, we apply the division lemma to 153 and 46, to get
153 = 46 x 3 + 15
Step 2: Since the reminder 46 ≠ 0, we apply division lemma to 15 and 46, to get
46 = 15 x 3 + 1
Step 3: We consider the new divisor 15 and the new remainder 1, and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 46 and 153 is 1
Notice that 1 = HCF(15,1) = HCF(46,15) = HCF(153,46) .
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Frequently Asked Questions on HCF of 506, 690, 153 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 506, 690, 153?
Answer: HCF of 506, 690, 153 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 690, 153 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 690, 153 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.