Highest Common Factor of 336, 966, 144, 37 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 336, 966, 144, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 966, 144, 37 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 336, 966, 144, 37 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 336, 966, 144, 37 is 1.
HCF(336, 966, 144, 37) = 1
HCF of 336, 966, 144, 37 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 966, 144, 37 is 1.
Highest Common Factor of 336,966,144,37 is 1
Step 1: Since 966 > 336, we apply the division lemma to 966 and 336, to get
966 = 336 x 2 + 294
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 294 and 336, to get
336 = 294 x 1 + 42
Step 3: We consider the new divisor 294 and the new remainder 42, and apply the division lemma to get
294 = 42 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 336 and 966 is 42
Notice that 42 = HCF(294,42) = HCF(336,294) = HCF(966,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 42, we apply the division lemma to 144 and 42, to get
144 = 42 x 3 + 18
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 18 and 42, to get
42 = 18 x 2 + 6
Step 3: We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 42 and 144 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(144,42) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37 > 6, we apply the division lemma to 37 and 6, to get
37 = 6 x 6 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 37 is 1
Notice that 1 = HCF(6,1) = HCF(37,6) .
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Frequently Asked Questions on HCF of 336, 966, 144, 37 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 336, 966, 144, 37?
Answer: HCF of 336, 966, 144, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 966, 144, 37 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 966, 144, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.