Highest Common Factor of 238, 372, 153, 688 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 238, 372, 153, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 238, 372, 153, 688 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 238, 372, 153, 688 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 238, 372, 153, 688 is 1.
HCF(238, 372, 153, 688) = 1
HCF of 238, 372, 153, 688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 238, 372, 153, 688 is 1.
Highest Common Factor of 238,372,153,688 is 1
Step 1: Since 372 > 238, we apply the division lemma to 372 and 238, to get
372 = 238 x 1 + 134
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 134 and 238, to get
238 = 134 x 1 + 104
Step 3: We consider the new divisor 134 and the new remainder 104, and apply the division lemma to get
134 = 104 x 1 + 30
We consider the new divisor 104 and the new remainder 30,and apply the division lemma to get
104 = 30 x 3 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 238 and 372 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(104,30) = HCF(134,104) = HCF(238,134) = HCF(372,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 153 > 2, we apply the division lemma to 153 and 2, to get
153 = 2 x 76 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 153 is 1
Notice that 1 = HCF(2,1) = HCF(153,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 1, we apply the division lemma to 688 and 1, to get
688 = 1 x 688 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 688 is 1
Notice that 1 = HCF(688,1) .
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Frequently Asked Questions on HCF of 238, 372, 153, 688 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 238, 372, 153, 688?
Answer: HCF of 238, 372, 153, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 238, 372, 153, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 238, 372, 153, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.