Highest Common Factor of 532, 352, 128, 998 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 532, 352, 128, 998 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 532, 352, 128, 998 is 2 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 532, 352, 128, 998 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 532, 352, 128, 998 is 2.
HCF(532, 352, 128, 998) = 2
HCF of 532, 352, 128, 998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 532, 352, 128, 998 is 2.
Highest Common Factor of 532,352,128,998 is 2
Step 1: Since 532 > 352, we apply the division lemma to 532 and 352, to get
532 = 352 x 1 + 180
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 180 and 352, to get
352 = 180 x 1 + 172
Step 3: We consider the new divisor 180 and the new remainder 172, and apply the division lemma to get
180 = 172 x 1 + 8
We consider the new divisor 172 and the new remainder 8,and apply the division lemma to get
172 = 8 x 21 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 532 and 352 is 4
Notice that 4 = HCF(8,4) = HCF(172,8) = HCF(180,172) = HCF(352,180) = HCF(532,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 128 > 4, we apply the division lemma to 128 and 4, to get
128 = 4 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 128 is 4
Notice that 4 = HCF(128,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 998 > 4, we apply the division lemma to 998 and 4, to get
998 = 4 x 249 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 998 is 2
Notice that 2 = HCF(4,2) = HCF(998,4) .
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Frequently Asked Questions on HCF of 532, 352, 128, 998 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 532, 352, 128, 998?
Answer: HCF of 532, 352, 128, 998 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 532, 352, 128, 998 using Euclid's Algorithm?
Answer: For arbitrary numbers 532, 352, 128, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.