Highest Common Factor of 969, 748, 737 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 969, 748, 737 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 969, 748, 737 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 969, 748, 737 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 969, 748, 737 is 1.
HCF(969, 748, 737) = 1
HCF of 969, 748, 737 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 969, 748, 737 is 1.
Highest Common Factor of 969,748,737 is 1
Step 1: Since 969 > 748, we apply the division lemma to 969 and 748, to get
969 = 748 x 1 + 221
Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 221 and 748, to get
748 = 221 x 3 + 85
Step 3: We consider the new divisor 221 and the new remainder 85, and apply the division lemma to get
221 = 85 x 2 + 51
We consider the new divisor 85 and the new remainder 51,and apply the division lemma to get
85 = 51 x 1 + 34
We consider the new divisor 51 and the new remainder 34,and apply the division lemma to get
51 = 34 x 1 + 17
We consider the new divisor 34 and the new remainder 17,and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 969 and 748 is 17
Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(85,51) = HCF(221,85) = HCF(748,221) = HCF(969,748) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 737 > 17, we apply the division lemma to 737 and 17, to get
737 = 17 x 43 + 6
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 6 and 17, to get
17 = 6 x 2 + 5
Step 3: 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 17 and 737 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(737,17) .
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Frequently Asked Questions on HCF of 969, 748, 737 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 969, 748, 737?
Answer: HCF of 969, 748, 737 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 969, 748, 737 using Euclid's Algorithm?
Answer: For arbitrary numbers 969, 748, 737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.