Highest Common Factor of 507, 312, 128 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 507, 312, 128 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 507, 312, 128 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 507, 312, 128 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 507, 312, 128 is 1.
HCF(507, 312, 128) = 1
HCF of 507, 312, 128 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 507, 312, 128 is 1.
Highest Common Factor of 507,312,128 is 1
Step 1: Since 507 > 312, we apply the division lemma to 507 and 312, to get
507 = 312 x 1 + 195
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 195 and 312, to get
312 = 195 x 1 + 117
Step 3: We consider the new divisor 195 and the new remainder 117, and apply the division lemma to get
195 = 117 x 1 + 78
We consider the new divisor 117 and the new remainder 78,and apply the division lemma to get
117 = 78 x 1 + 39
We consider the new divisor 78 and the new remainder 39,and apply the division lemma to get
78 = 39 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 507 and 312 is 39
Notice that 39 = HCF(78,39) = HCF(117,78) = HCF(195,117) = HCF(312,195) = HCF(507,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 128 > 39, we apply the division lemma to 128 and 39, to get
128 = 39 x 3 + 11
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 11 and 39, to get
39 = 11 x 3 + 6
Step 3: We consider the new divisor 11 and the new remainder 6, and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 39 and 128 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(39,11) = HCF(128,39) .
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Frequently Asked Questions on HCF of 507, 312, 128 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 507, 312, 128?
Answer: HCF of 507, 312, 128 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 507, 312, 128 using Euclid's Algorithm?
Answer: For arbitrary numbers 507, 312, 128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.