Highest Common Factor of 661, 916 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 661, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 916 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 661, 916 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 661, 916 is 1.
HCF(661, 916) = 1
HCF of 661, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 916 is 1.
Highest Common Factor of 661,916 is 1
Step 1: Since 916 > 661, we apply the division lemma to 916 and 661, to get
916 = 661 x 1 + 255
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 255 and 661, to get
661 = 255 x 2 + 151
Step 3: We consider the new divisor 255 and the new remainder 151, and apply the division lemma to get
255 = 151 x 1 + 104
We consider the new divisor 151 and the new remainder 104,and apply the division lemma to get
151 = 104 x 1 + 47
We consider the new divisor 104 and the new remainder 47,and apply the division lemma to get
104 = 47 x 2 + 10
We consider the new divisor 47 and the new remainder 10,and apply the division lemma to get
47 = 10 x 4 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 916 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(47,10) = HCF(104,47) = HCF(151,104) = HCF(255,151) = HCF(661,255) = HCF(916,661) .
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Frequently Asked Questions on HCF of 661, 916 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 661, 916?
Answer: HCF of 661, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.