Highest Common Factor of 988, 428, 661, 354 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 988, 428, 661, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 428, 661, 354 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 988, 428, 661, 354 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 988, 428, 661, 354 is 1.
HCF(988, 428, 661, 354) = 1
HCF of 988, 428, 661, 354 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 988, 428, 661, 354 is 1.
Highest Common Factor of 988,428,661,354 is 1
Step 1: Since 988 > 428, we apply the division lemma to 988 and 428, to get
988 = 428 x 2 + 132
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 132 and 428, to get
428 = 132 x 3 + 32
Step 3: We consider the new divisor 132 and the new remainder 32, and apply the division lemma to get
132 = 32 x 4 + 4
We consider the new divisor 32 and the new remainder 4, and apply the division lemma to get
32 = 4 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 988 and 428 is 4
Notice that 4 = HCF(32,4) = HCF(132,32) = HCF(428,132) = HCF(988,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 661 > 4, we apply the division lemma to 661 and 4, to get
661 = 4 x 165 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 661 is 1
Notice that 1 = HCF(4,1) = HCF(661,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get
354 = 1 x 354 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1
Notice that 1 = HCF(354,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 988, 428, 661, 354 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 988, 428, 661, 354?
Answer: HCF of 988, 428, 661, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 428, 661, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 428, 661, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.